Notices
Results 1 to 9 of 9

Thread: Partialintegration help

  1. #1 Partialintegration help 
    Forum Freshman
    Join Date
    Nov 2006
    Posts
    10
    I'm having some math problems here which I don't know how to solve, I'm really clueless.

    I don't have any program that can display integrals and stuff like that, maybe a tip on any? Also I'm not native English.

    1)
    Find the primitive function for e^(x) * cos (x)

    2)
    Find the primitive to x / ( cos(x) ^2 )

    3)
    Find the primitive to e^( sqrt(x) ) with 1 as higher boundary and 0 as lower.
    Hint: substitute with t = sqrt(x)

    Any help is really appreciated.


    Every action causes an equal and opposite reaction
    Reply With Quote  
     

  2.  

    Related Discussions:

       

    • #2  
      Forum Professor serpicojr's Avatar
      Join Date
      Jul 2007
      Location
      JRZ
      Posts
      1,069
      Well, we don't mind helping out with homework, but we'll only help if you have made an honest effort yourself and show us what you have tried.

      Having a program which can integrate things for you is a crutch that will only prevent you from learning to trust your own abilities at integration. So look at it as a blessing that you haven't been spoiled by such.

      So what have you done so far?


      Reply With Quote  
       

    • #3  
      Forum Freshman
      Join Date
      Nov 2006
      Posts
      10
      Great!

      I wasn't thinking of a program to solve them for me, only something to display the integrals. Kinda like:

      http://upload.wikimedia.org/math/9/1...ac8648a1f7.png - borrowed from wiki.

      I type int()dx for the integration for now

      1)
      int( e^(x) * cos(x) )dx = e^(x) * sin(x) - int( e^(x) * sin(x) )dx = e^(x) * sin(x) - ( - e^(x) * cos(x) - int( - e^(x) * cos(x) )dx = e^(x) * (sin(x) + cos(x) ) - int( e^(x) * cos(x) )dx.

      The last is where I'm sure I went wrong, cause that would mean it's endless going between 0 and 1 or something...

      At first I did something like this:
      int( e^(x) * cos(x) )dx = e^(x) * sin(x) - int( e^(x) * sin(x) )dx
      After you could break out e^(x) from int( e^(x) * sin(x) )dx and get the answer e^(x) * ( sin(x) + cos(x) ) + C.

      This is almost correct, only that the answer should be 1/2 times that... this is how far I came with this.

      2)
      int( x / ( cos(x)^2 )dx = int( x * 1 / ( cos(x)^2 ) )dx. Here I need to find the integration of 1 / ( cos(x)^2 ) which can't figure out how to do really. First I tried to substitute cos(x)^2 with t and got ln (t) but the answer surely can't be ln( cos(x)^2 ) to that.

      3)
      Here I'm just stuck trying to substitute the sqrt(x). If t = sqrt(x) then dt/dx = 1 / ( 2sqrt(x) ). But how you get e^( sqrt(x) ) * dx to match there I'm lost.
      Every action causes an equal and opposite reaction
      Reply With Quote  
       

    • #4  
      Forum Ph.D.
      Join Date
      Apr 2008
      Posts
      956
      Quote Originally Posted by Blob
      Here I need to find the integration of 1 / ( cos(x)^2 ) which can't figure out how to do really.
      1 ⁄ cos<sup>2</sup>(x) = sec<sup>2</sup>(x)

      Does that ring a bell?
      Reply With Quote  
       

    • #5  
      Forum Freshman
      Join Date
      Nov 2006
      Posts
      10
      Quote Originally Posted by JaneBennet
      Quote Originally Posted by Blob
      Here I need to find the integration of 1 / ( cos(x)^2 ) which can't figure out how to do really.
      1 ⁄ cos<sup>2</sup>(x) = sec<sup>2</sup>(x)

      Does that ring a bell?
      Sec? err not really
      Every action causes an equal and opposite reaction
      Reply With Quote  
       

    • #6  
      Forum Ph.D.
      Join Date
      Apr 2008
      Posts
      956
      sec = secant = 1 ⁄ cosine

      Hint: Differentiate tan(x). What do you get?
      Reply With Quote  
       

    • #7  
      Forum Freshman
      Join Date
      Nov 2006
      Posts
      10
      I get 1 + tan<sup>2</sup>(x). I think I know where you're going; that it's somehow connected but I can't make the connection =/

      Edit: Oh man it suddenly dawned to me that it's the same as 1 / cos<sup>2</sup>(x), which means that...

      int( x / cos<sup>2</sup>(x )dx = x * tan(x) - int( tan(x) )dx

      This however brings up a new problem: finding primitive to tan(x).

      int( sin(x) * 1 / cos(x) )dx = -cox(x) * 1 / cos(x) - int( -cos(x) * - 1 / sin<sup>2</sup>(x) )dx = -1 + int( cos(x) / sin<sup>2</sup>(x) )dx

      Which leaves me stuck yet again, damnet =/
      Every action causes an equal and opposite reaction
      Reply With Quote  
       

    • #8  
      Forum Freshman
      Join Date
      Nov 2006
      Posts
      10
      I found the solutions the the problems now =)
      Every action causes an equal and opposite reaction
      Reply With Quote  
       

    • #9  
      Forum Ph.D.
      Join Date
      Apr 2008
      Posts
      956
      Quote Originally Posted by Blob
      This however brings up a new problem: finding primitive to tan(x).
      tan(x) = sin(x)*⁄*cos(x) = −[−sin(x) ⁄ cos(x)]

      and the expression in the square brackets is of the form f′(x)*⁄*f(x). You should know how to integrate expressions of the form f′(x)*⁄*f(x).
      Reply With Quote  
       

    Bookmarks
    Bookmarks
    Posting Permissions
    • You may not post new threads
    • You may not post replies
    • You may not post attachments
    • You may not edit your posts
    •