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Thread: Calculus

  1. #1 Calculus 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    just until yesterday i thought i was alright at calculus until i saw this very fundamental calculus question which i couldn't solve.

    can anyone help me?




    thank you.


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  3. #2  
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    http://www.wolframalpha.com/


    I'm a refugee from /sci/
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  4. #3  
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    I think you have to change the equation to be expressed in terms of theta....
    (runs to get her calc book)
    I just got a C in my calc III class, I was disappointed. My teacher sucked.
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  5. #4  
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    taking a quick glance at it, id say to use Partial Fractions then integrate as two separate integrals

    1/(1+cos(x)) and 1/(1+sin(x))

    using MAPLE, integrating produces

    tan(1/2(x)) - 2/[tan(1/2(x)) + 1] evaluated from 0 to pi
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  6. #5 Re: Calculus 
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    Quote Originally Posted by Heinsbergrelatz
    just until yesterday i thought i was alright at calculus until i saw this very fundamental calculus question which i couldn't solve.

    can anyone help me?




    thank you.

    =
    =
    =
    =
    =1
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  7. #6 Re: Calculus 
    Forum Freshman pbandjay's Avatar
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    Quote Originally Posted by DrRocket

    =
    Doesn't that denominator equal 1 + cos(x) + sin(x) + cos(x)sin(x)?
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  8. #7  
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    it does, I have a feeling Dr. Rocket intended to make that mistake to see if we were paying attention.











    let then;

    so;





    And I believe this is much easier to solve, provided I made no mistakes. And it is;

    Wise men speak because they have something to say; Fools, because they have to say something.
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  9. #8 Re: Calculus 
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    Quote Originally Posted by pbandjay
    Quote Originally Posted by DrRocket

    =
    Doesn't that denominator equal 1 + cos(x) + sin(x) + cos(x)sin(x)?
    Yep, I must have been tired when I looked at the problem.

    But the integral after the mistake is more interesting.
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  10. #9  
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    Quote Originally Posted by Arcane_Mathematician





    Could someone explain this step?

    I'm not very good at this trig stuff
    OK I found sin 2 x = 2 sin x cos x which might help.

    I would go

    8( 2/sin^2@ - 1/sin2@ - 2root(2)/cos^2@sin@)

    OR 8( 2/sin^2@ - 1/2sin@cos@ - 2root(2)/cos^2@sin@)

    Sorry I can't use the 'tex' thing properly!!

    Trying now!!

    Note the @ are theta (now fixed!!)



    Actually when I first though it I though this is like integrating 1/u to log(u)

    Could I do that?

    When I say 'I' I mean could anyone (who is better at maths than me) do that?
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  11. #10  
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    Quote Originally Posted by smokey
    Quote Originally Posted by Arcane_Mathematician





    Could someone explain this step?
    Quote Originally Posted by Arcane_Mathematician
    it does, I have a feeling Dr. Rocket intended to make that mistake to see if we were paying attention.











    let then;

    the first half of my post was the explanation of that step
    Wise men speak because they have something to say; Fools, because they have to say something.
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  12. #11  
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    Quote Originally Posted by Arcane_Mathematician





    And I believe this is much easier to solve, provided I made no mistakes. And it is;

    I meant this bit, seems I may have quoted the wrong line.

    For the second line I would get
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  13. #12  
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    Thank you smokey. I made an arithmetic error earlier that I didn't catch. Working it all out here, I believe I was able to see it.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  14. #13  
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    Sorry for my late appreciation to all the members who helped me with this question, it was cause i was going to solve mine and compare the workings.

    anyway i got to a similar approach and got a similar answer, but not exactly same, but i will still work on that


    anyway thanks alot.
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  15. #14  
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    post your work, I'm not 100% sure I did it right, and your answer may be more solid.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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    its really a informative post...
    thanks for your information ...........
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  17. #16  
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    then you just apply the limits. does it look alright?
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  18. #17  
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    how did you get to that starting point?
    Wise men speak because they have something to say; Fools, because they have to say something.
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  19. #18  
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    how did you get to that starting point?
    i just did simplified it using partial fractions from the original integral.
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  20. #19  
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    Quote Originally Posted by Heinsbergrelatz
    how did you get to that starting point?
    i just did simplified it using partial fractions from the original integral.
    I can't figure out how you used partial fractions for this one. It isn't registering for me, could you post all of the steps you used to arrive at this conclusion?
    Wise men speak because they have something to say; Fools, because they have to say something.
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  21. #20  
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    Hey arcane, here is my working alittle modified and easier actually, though the post is a little late, just see if you agree with it.

    okay this little nasty integral needed some decent amount of trigonometric to "t-substitution method"
















    okay because now we have inserted:




    its pretty tedious to try and make "t" the subject of the formula and plug it in to our integral right? so how about this?

    since the bounds were





    so our new Up. and Lower bounds are:


    i would appreciate any corrections to my mistakes.
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  22. #21  
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    +12=13
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  23. #22  
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    Quote Originally Posted by ismaeljohnson11
    +12=13
    No.

    Proof:



    QED

    Rather, +12 is all values that are greater than 12. If we consider the natural numbers than it would be the set A, for all A = {13, 14, 15,...}. On the other hand, if we are considering real numbers, than it would be x, for all x greater than 12, that is to say decimals other than zero are allowed (e.g., 12.1, 12.01, 12.001, etc...).
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