Results 1 to 15 of 15

Math Help - double-parted integral

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    23

    double-parted integral

    Hello! i'm having some trouble with this question(attached file). Can someone explain the steps to remove the..foreign variable. thank you in advance
    Attached Thumbnails Attached Thumbnails double-parted integral-sem-titulo.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Corum View Post
    Hello! i'm having some trouble with this question(attached file). Can someone explain the steps to remove the..foreign variable. thank you in advance
    Is this really the whole question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    23
    Yes. Calculate: *whats there*
    seeing as it's in that interval, i suppose calculating the numeric value in t, which then multiplies the rest. the problem is that the upper limit is x...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Corum View Post
    Yes. Calculate: *whats there*
    seeing as it's in that interval, i suppose calculating the numeric value in t, which then multiplies the rest. the problem is that the upper limit is x...
    No, the problem is that \int\frac{\cos(t)}{t}dt is not expressible in elementary terms.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    23
    Ci(t). But if the limit was [0, PI] for ex.

    d/dx ( \int ln (t) dt) = ln x

    Along these lines?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Corum View Post
    Ci(t). But if the limit was [0, PI] for ex.

    d/dx ( \int ln (t) dt) = ln x

    Along these lines?
    I have no idea what you are talking about.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2010
    Posts
    23
    An example of the Fundamental theorem of calculus
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Corum View Post
    An example of the Fundamental theorem of calculus
    There is no differential operator here. How could you possibly hope to apply the FTC?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jan 2010
    Posts
    23
    Not along those lines then. Thanks! Any other suggestion how to approach it?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Corum View Post
    Not along those lines then. Thanks! Any other suggestion how to approach it?
    I don't any see possible way to do this. Maybe I am missing some little trick or something, but I have a feeling that this either isn't the whole problem or you wrote it wrong.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Jan 2010
    Posts
    23
    sorry there, but i'm sure i didnīt make a mistake.
    heres the whole exercice:
    Attached Thumbnails Attached Thumbnails double-parted integral-sem-titulo.jpg  
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Drexel28 View Post
    I don't any see possible way to do this. Maybe I am missing some little trick or something, but I have a feeling that this either isn't the whole problem or you wrote it wrong.
    Maybe let u=\int_1^x\frac{\cos t}{t}\,dt\implies \,du=\frac{\cos x}{x}\,dx

    So \int\frac{\cos x}{x}\left(\int_1^x\frac{\cos t}{t}\,dt\right)^4\,dx\xrightarrow{u=\int_1^x\frac  {\cos t}{t}\,dt}{}\int u^4\,du

    Is this what is needed?
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Chris L T521 View Post
    Maybe let u=\int_1^x\frac{\cos t}{t}\,dt\implies \,du=\frac{\cos x}{x}\,dx

    So \int\frac{\cos x}{x}\left(\int_1^x\frac{\cos t}{t}\,dt\right)^4\,dx\xrightarrow{u=\int_1^x\frac  {\cos t}{t}\,dt}{}\int u^4\,du

    Is this what is needed?
    But you will still have to compute the integral at the end. I guess that makes sense. Good-eye!
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Drexel28 View Post
    But you will still have to compute the integral at the end. I guess that makes sense. Good-eye!
    True..but at least it reduces it...to something that can't be done in terms of elementary functions...
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Newbie
    Joined
    Jan 2010
    Posts
    23
    Yes, I've solved it now. That form is the excepted. Thanks for the help =)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 2nd 2010, 02:25 AM
  2. Double integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 13th 2010, 09:33 AM
  3. Double Integral and Triple Integral question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 12:47 PM
  4. Double integral (iterated integral)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 7th 2009, 04:01 PM
  5. Replies: 6
    Last Post: May 18th 2008, 06:37 AM

Search Tags


/mathhelpforum @mathhelpforum