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Thread: A very tricky integral

  1. #1 A very tricky integral 
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    this is a question which i stumbled upon two days ago, and i am having some trouble on it. I would appreciate if anyone could give me some hint or any clue to the question.

    assuming:



    thus integrate the following integral;



    so far i was able to differentiate the given "y" and got this:



    where i think Q(x) is a cubic polynomial. Then i tried to relate the integral with my derivative but it doesn't seem all that easy, or maybe it is just that i cant see it. Can anyone please help me out?

    thank you


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  3. #2  
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    Your derivative looks wrong.



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  4. #3  
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    Your derivative looks wrong.
    i dont think so, im pretty sure its correct. i just represented the tedious cubic polynomial in to Q(x). What did you get?
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  5. #4  
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    Quote Originally Posted by Heinsbergrelatz
    Your derivative looks wrong.
    i dont think so, im pretty sure its correct. i just represented the tedious cubic polynomial in to Q(x). What did you get?
    Well, for one thing,

    Also,

    And; for as well as





    Power, product, and Chain rules apply.



    Notice that there are three terms. The only like term amongst all three terms is e^{bx}. You differentiated wrong, altogether. I have NO idea how you got what you got. You need to post your steps.
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  6. #5  
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    im not saying im wrong or im not saying im correct, but here is how i did it.

    first of all

    i clearly know the derivative of e^ax so you dont need to mention that and the other corrections you listed.

    now this is obviosuly a job for the product rule :












    i did alittle common factoring, and you need to common factor to get what i got as showed in the steps. Plus your third part is wrong, its supposed to be "x" not "2x"
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  7. #6  
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    Quote Originally Posted by Arcane_Mathematician


    Notice that there are three terms. The only like term amongst all three terms is e^{bx}. You differentiated wrong, altogether. I have NO idea how you got what you got. You need to post your steps.
    is common and that will allow the proposed expression to hold.

    How that helps with the integral is a bit of a mystery. A bigger mystery is why one cares about that hideous integral.
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  8. #7  
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    Woops I forgot to seperate it out into seperate terms when doing the product rule.

    Not sure how I managed that. I was doing product rules earlier that day too!

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  9. #8  
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    is common and that will allow the proposed expression to hold.

    How that helps with the integral is a bit of a mystery. A bigger mystery is why one cares about that hideous integral.
    apparently this integral is indeed pretty hideous even the examiners from the Cambridge itself agreed. im quoting this from the examination report, in which the examiners themeselves said:

    "In many ways, this question is little more than an academic exercise, since I can see no way in which these integrals would actually arise in any practical situation. I apologise for this. However, it was a good test of candidates’ ability to stretch a general result in different directions, probing them for increasing amounts of insight and perseverance."

    Oo and Dr.Rocket, instead of saying its hideous and whatever, why dont you try and help me with the question. Yes i know it is not a pleasant integral to solve, thats why they gave you an original function to start with. Otherwise why would the examiners from Cambridge give such a function? obviously the integral alone is too complicated and unrealistic to be solved, thus its a hint.
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  10. #9 Re: A very tricky integral 
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    Quote Originally Posted by Heinsbergrelatz
    this is a question which i stumbled upon two days ago, and i am having some trouble on it. I would appreciate if anyone could give me some hint or any clue to the question.

    assuming:



    thus integrate the following integral;



    so far i was able to differentiate the given "y" and got this:



    where i think Q(x) is a cubic polynomial. Then i tried to relate the integral with my derivative but it doesn't seem all that easy, or maybe it is just that i cant see it. Can anyone please help me out?

    thank you
    I'm more concerned about how long you've studied calculus of one variable yet still incorrectly differentiated a simple function. Back to the basics.

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    Im more concerned about how long you've studied calculus of one variable yet still incorrectly differentiated a simple function. Back to the basics.
    aren't you embarrassed to say this? because quite frankly you are the one who cannot understand my working hence determining that it is wrong when in fact my derivative is correct. You on the other hand did something in which any single variable calculus student can do, instead of simply differentiating a function, you just d/dx(...) which one might suspect that you are the one who cannot differentiate the basic functions.

    in conclusion, Ellatha, check my workings again, and then tell me who is right or wrong, otherwise your post now stands as nothing but an unorthodox one.

    Why do people say my derivative is Wrong? i mean clearly its CORRECT., i mean i even showed the steps, and yet i have people saying i dont know the basics and im wrong and blah blah...
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  12. #11  
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    Quote Originally Posted by Heinsbergrelatz
    Im more concerned about how long you've studied calculus of one variable yet still incorrectly differentiated a simple function. Back to the basics.
    aren't you embarrassed to say this? because quite frankly you are the one who cannot understand my working hence determining that it is wrong when in fact my derivative is correct. You on the other hand did something in which any single variable calculus student can do, instead of simply differentiating a function, you just d/dx(...) which one might suspect that you are the one who cannot differentiate the basic functions.

    in conclusion, Ellatha, check my workings again, and then tell me who is right or wrong, otherwise your post now stands as nothing but an unorthodox one.

    Why do people say my derivative is Wrong? i mean clearly its CORRECT., i mean i even showed the steps, and yet i have people saying i dont know the basics and im wrong and blah blah...
    Why would I be embarrased? I posted the method that any student competent in single-variable calculus can do. This is what you should have done, then simplified. It's interesting how previously you stated that you did not claim to be correct or incorrect, now write that you are "clearly correct."
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  13. #12  
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    Quote Originally Posted by Heinsbergrelatz
    Oo and Dr.Rocket, instead of saying its hideous and whatever, why dont you try and help me with the question. Yes i know it is not a pleasant integral to solve, thats why they gave you an original function to start with. Otherwise why would the examiners from Cambridge give such a function? obviously the integral alone is too complicated and unrealistic to be solved, thus its a hint.
    Because it is a hideous and uninteresting question and so I don't care what the answer is. I care even less about the opinion of "examiners from Cambridge."

    It looks tedious but doable. I no longer have to engage in tedium if I don't want to, and I certainly don't want to.

    It's your problem. Solve it yourself.
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  14. #13  
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    Because it is a hideous and uninteresting question and so I don't care what the answer is. I care even less about the opinion of "examiners from Cambridge."

    It looks tedious but doable. I no longer have to engage in tedium if I don't want to, and I certainly don't want to.

    It's your problem. Solve it yourself.
    Wow, this is science forum, where i thought people help each other with problems they have or at least discuss about it, not leave a post saying its uninteresting, tedious thus he/she doesn't want to solve it, or saying one is wrong when actually they are completely right.

    Next time if you are not even interested in helping me and just wanting to leave those remarks of yours (uninteresting, tedious or whatever) dont even bother to post on my thread at all.

    thanks.
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  15. #14  
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    Quote Originally Posted by Heinsbergrelatz
    Next time if you are not even interested in helping me and just wanting to leave those remarks of yours (uninteresting, tedious or whatever) dont even bother to post on my thread at all.

    thanks.
    You are in no position to be giving orders to anyone.

    You asked a question. Don't do that if you can't stand the answer.
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  16. #15  
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    Rocket man gets to insult anyone, whether it's justified or not. He has ruined this forum and continues to harass people without restraint.

    Heinsbergrelatz, you responded appropriately.
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  17. #16  
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    Quote Originally Posted by Ots
    Rocket man gets to insult anyone, whether it's justified or not. He has ruined this forum and continues to harass people without restraint.

    Heinsbergrelatz, you responded appropriately.
    It is most gratifying to see umbrage being taken by someone of your ilk.
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  18. #17  
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    The Science Forum - Scientific Discussion and Debate
    I think a few regular members are starting to get slightly fed up with these sort of threads as they are all "help me solve this" as opposed to "can you help me understand the underlying idea". The former do not generate interesting discussions.

    This is an internet forum, ie- a place where people can discuss things. It should not be used purely as a free homework clinic. Clearly there will be threads started where people aren't sure how to solve a question, but those sort of threads shouldn't be occuring on a regular basis from an individual.

    Also, this is an online "community". There should be a balance of give and take by all members.

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  19. #18  
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    Quote Originally Posted by sox
    The Science Forum - Scientific Discussion and Debate
    I think a few regular members are starting to get slightly fed up with these sort of threads as they are all "help me solve this" as opposed to "can you help me understand the underlying idea". The former do not generate interesting discussions.

    This is an internet forum, ie- a place where people can discuss things. It should not be used purely as a free homework clinic. Clearly there will be threads started where people aren't sure how to solve a question, but those sort of threads shouldn't be occuring on a regular basis from an individual.

    Also, this is an online "community". There should be a balance of give and take by all members.
    Well understood. But continual insults (not by you) don't lend themselves to give and take. They stifle discussion.

    Personally I don't care about rocket. There are lots of people like that in the world. But I sometimes follow posts in this forum and it really gets tiring when a thread gets going and all of a sudden, here comes rocket man to jump in and tell someone they don't know what they are talking about or that they need to go learn this or that. Hey, contribute or go elsewhere. That's all Heinsbergrelatz was saying, and he's right. The 'bashing' isn't appreciated.
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  20. #19  
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    Why would I be embarrased? I posted the method that any student competent in single-variable calculus can do. This is what you should have done, then simplified. It's interesting how previously you stated that you did not claim to be correct or incorrect, now write that you are "clearly correct."
    yes exactly thats what i have done, and yet you couldn't understand my workings. Bottom line, you are wrong for saying that my derivative is wrong.

    I think you need some S.V.C revision.

    You are in no position to be giving orders to anyone.

    You asked a question. Don't do that if you can't stand the answer.
    umm... No thats not it. And also your last sentence replies probably only to "your" answers. You see the thing is I dont care if YOU think its hideous or not, my purpose of this question was to get some decent help for this question and clearly NO ONE has done so, out of all these 7 posts. All i have got was people doubting my derivative in which clearly they themselves were the falsified ones. obviously if this was an easier integral, posts of answers would have been given, in REPETITIONS. But clearly this is not the case. In conclusion this thread renders almost all replies useless for the following reasonsL
    -unwanted opinions from a member ( i dont need to mention his name again)
    -claiming that others are wrong when they themselves are
    -clearly as time passes posts are moving further away from the core of my question.


    Hey, contribute or go elsewhere..... The 'bashing' isn't appreciated.
    Ots, apparently some people just dont understand this.


    but those sort of threads shouldn't be occuring on a regular basis from an individual.
    Yes Sox i clearly understand your point, but at least i dont give replies to posts simply saying that others are wrong, when they havent double checked for themselves.
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  21. #20  
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    Quote Originally Posted by Heinsbergrelatz
    Why would I be embarrased? I posted the method that any student competent in single-variable calculus can do. This is what you should have done, then simplified. It's interesting how previously you stated that you did not claim to be correct or incorrect, now write that you are "clearly correct."
    yes exactly thats what i have done, and yet you couldn't understand my workings. Bottom line, you are wrong for saying that my derivative is wrong.

    I think you need some S.V.C revision.

    You are in no position to be giving orders to anyone.

    You asked a question. Don't do that if you can't stand the answer.
    umm... No thats not it. And also your last sentence replies probably only to "your" answers. You see the thing is I dont care if YOU think its hideous or not, my purpose of this question was to get some decent help for this question and clearly NO ONE has done so, out of all these 7 posts. All i have got was people doubting my derivative in which clearly they themselves were the falsified ones. obviously if this was an easier integral, posts of answers would have been given, in REPETITIONS. But clearly this is not the case. In conclusion this thread renders almost all replies useless for the following reasonsL
    -unwanted opinions from a member ( i dont need to mention his name again)
    -claiming that others are wrong when they themselves are
    -clearly as time passes posts are moving further away from the core of my question.


    Hey, contribute or go elsewhere..... The 'bashing' isn't appreciated.
    Ots, apparently some people just dont understand this.


    but those sort of threads shouldn't be occuring on a regular basis from an individual.
    Yes Sox i clearly understand your point, but at least i dont give replies to posts simply saying that others are wrong, when they havent double checked for themselves.
    Good points.

    Hopefully now we can move on in a more positive fashion.

    Happy holidays!
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    Good points.

    Hopefully now we can move on in a more positive fashion.

    Happy holidays!
    im sure Doc. will comeback with something not pleasant again. But till then happy holidays to you too
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  23. #22  
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    Come, come, this is supposed to be the season of goodwill!

    I take no sides in this silly quarrel, I merely point out the following:

    DrRocket is a highly respected and valued member of this forum. If he expresses himself rather bluntly at times, that is the price our pride has to pay for his wisdom. I myself have been on the receiving end of his bluntness; I didn't like it at the time, but I grew out of it.

    Second, there is a world of difference between asking for the solution to a particular equation (say) and asking for clarification about a piece of theory that one may have heard in class or have found in a book or (heaven help us) on the internet. The former question can expect the answer "right" or "wrong". The latter will usually be treated more fulsomely here. ("New theories" are, of course, another matter)

    Finally, those of us "elder statesmen" who received their early education without the benefit of the internet are, and must be, on the alert for those registered users AND lurkers who try to short-cut their true understanding by looking at sites like these.

    Given that there are those who will try this nonetheless, it seems almost like a DUTY to say clearly whenever a post is wrong; lurkers - homework shirkers - are not interested in discussions, they want the answer on a plate NOW.

    Umm. It seems like I did take sides after all. But those are my opinions, though I meant no harm to anyone here
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  24. #23  
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    DrRocket is a highly respected and valued member of this forum. If he expresses himself rather bluntly at times, that is the price our pride has to pay for his wisdom. I myself have been on the receiving end of his bluntness; I didn't like it at the time, but I grew out of it.
    How can anyone ever get any sense of respect when they themselves dont respect certain members of this forum? I don't just hate his numb, rude replies, i absolutely disgust it. Yes you might have grown out of it, but im far from being in that situation. Yes he might be smart, and have an extensive knowledge in the subject but that is no way to address certain members of this forum(im not only referring to myself).

    Given that there are those who will try this nonetheless, it seems almost like a DUTY to say clearly whenever a post is wrong; lurkers - homework shirkers - are not interested in discussions, they want the answer on a plate NOW.
    I hope you are not referring this to me because, almost every time i need help with a question, i get one or two suitable answers which has some relation to my question, but eventually i get get fed up and i come up with the answers, because no one actually does give me a useful feedback, so i post my answers online, and i ask for corrections to those more experienced, but as always i get few or no response from there.

    Just for your information Guitarist, i never ask Maths hmwrk questions in the forum, hmwrk problems in school are simply too elementary, and so I do not need to waste my time posting it up in the first place. I post problems which i find challenging from other sources, and through that post i would love to discuss about the question, as others might also find it interesting. But how on earth can i show the depth of interest to my own question, and get the motivation to discuss about it when half of the posts are absolutely meaningless and not to mention are "hideous and not interesting?"
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  25. #24  
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    Quote Originally Posted by Guitarist
    Come, come, this is supposed to be the season of goodwill!

    I take no sides in this silly quarrel, I merely point out the following:

    DrRocket is a highly respected and valued member of this forum. If he expresses himself rather bluntly at times, that is the price our pride has to pay for his wisdom. I myself have been on the receiving end of his bluntness; I didn't like it at the time, but I grew out of it.
    You are rationalizing inappropriate behavior.

    His math contributions to the forum are valuable to be sure.

    But this does not license him to do the other things he does.
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  26. #25  
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    Quote Originally Posted by Heinsbergrelatz
    ]

    How can anyone ever get any sense of respect when they themselves dont respect certain members of this forum? I don't just hate his numb, rude replies, i absolutely disgust it. Yes you might have grown out of it, but im far from being in that situation. Yes he might be smart, and have an extensive knowledge in the subject but that is no way to address certain members of this forum(im not only referring to myself).
    I am just real damn sorry if the realization that you have posed an uninteresting question has bruised your little ego. Excuse me all to hell.

    But if you are that delicate you ought to consider university study in something other than mathematics.
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  27. #26  
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    You miss the point Heisenbergrelatz.

    The reason you are getting few responses is because there is no variation in your posts and people are not interested in solving random, tedious calculations.

    If you look back through the maths forum, just about all your threads are asking for help to solve a problem, usually an integration. People generally aren't interested in doing some random and complicated calculation.

    The fact that these sort of problems are being posted so frequently gives the impression that you haven't really understood and/or digested the principles involved and this can irritate people in the know who are expected to answer.

    You would find that the people on this board who can help you would be more accomodating if you showed an understanding of the mathematics.

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  28. #27  
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    I am just real damn sorry if the realization that you have posed an uninteresting question has bruised your little ego. Excuse me all to hell.

    But if you are that delicate you ought to consider university study in something other than mathematics.
    Whatever, you can use all the hells you want, with whatever unpleasant things you got there, but i ain't taking any suggestions of yours.

    You miss the point Heisenbergrelatz.

    The reason you are getting few responses is because there is no variation in your posts and people are not interested in solving random, tedious calculations.

    If you look back through the maths forum, just about all your threads are asking for help to solve a problem, usually an integration. People generally aren't interested in doing some random and complicated calculation.

    The fact that these sort of problems are being posted so frequently gives the impression that you haven't really understood and/or digested the principles involved and this can irritate people in the know who are expected to answer.

    You would find that the people on this board who can help you would be more accomodating if you showed an understanding of the mathematics.
    Its cause, this whole numerical integral questions just hit me with new surprises everyday. You see i dont just stick to one source of textbook. Textbooks used in school are way too easy so then i get something more complicated to challenge my further understanding of the integrals. I actually quite understand the derivatives and integrals by now, pretty well, in the Single variable sense of course. And yes, i do post alot of integral questions, and maybe people find them rather tedious and boring. If so, why dont you guys just say its boring in the first place, before YOU (Sox) start telling me im wrong when im telling you for the third time already, you are not the correct one.

    Maybe you should start understanding before you start replying to other people.
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  29. #28  
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    Mod hat: This thread is getting bad-tempered and nothing to do with the subject heading. This pointless bickering also goes against the spirit of this sub-forum.

    Just all settle down, eat a mince pie (or two) and decide between yourselves where you want this thread to go.
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  30. #29  
    sox
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    Quote Originally Posted by Heinsbergrelatz
    before YOU (Sox) start telling me im wrong when im telling you for the third time already, you are not the correct one.

    Maybe you should start understanding before you start replying to other people.
    If you look back to my original post I was trying to offer you advice about why you hadn't solved the problem. I made a mistake as I then went on to say a bit further down the page. People make mistakes, especially when theyr'e tired.

    Maybe YOU should be more gracious when someone has genuinely tried to help you, even if in the end, they weren't any use.

    Out of respect for the moderator I shall say no more and retreat to a thread where actual mathematical constructs are in duscussion.

    p.s - when it comes to mince pies, you should always take two. It would be rude not to!

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  31. #30  
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    Ok Sox..... its a new year. Lets drop everything, and start fresh. Dr.Rocket, i dont know if its okay with you, but if you think i may have been rude, well then my apologies to you. No hard feelings alright? We are all members in a scientific community(forum), and hopefully in this novel year, we can help each other discuss many questions and problems that will follow.

    Peace to all, and Happy new Year :-D
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