Results 1 to 6 of 6

Math Help - 2 integration by parts problems

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    36

    2 integration by parts problems

    1) \int_{0}^{\frac{\pi }{2}}x^2 cos2x dx
    2) \int_{0 }^{\pi }e^x sin2x dx

    work iv done so far.
    1) uv-\int v du
    \frac{x}{2}sin 2x -\int x sin 2x dx
    2) uv-\int v du
    sin 2x e^x-\int e^x \frac{1}{2} cos 2x dx

    am i doing these right? I think i am doing them wrong can anyone help?
    thanks for the help in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by dandaman View Post
    1) \int_{0}^{\frac{\pi }{2}}x^2 cos2x dx
    2) \int_{0 }^{\pi }e^x sin2x dx

    work iv done so far.
    1) uv-\int v du
    \frac{x^{{\color{red}2}}}{2}sin 2x -\int x sin 2x dx
    2) uv-\int v du
    sin 2x e^x-\int e^x \frac{1}{2} cos 2x dx

    am i doing these right? I think i am doing them wrong can anyone help?
    thanks for the help in advance
    You're doing them right (except note the correction in red)! Now apply integration by parts to \int x\sin\left(2x\right)\,dx and e^x\cos\left(2x\right)\,dx
    Last edited by Chris L T521; August 31st 2009 at 07:47 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2009
    Posts
    71
    I think for number 1 he lost an x.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2009
    Posts
    36
    k thanks for the response I got -pi/4 for #1
    but for #2, i cant get the answer.
    this is what i get and can't continue from here.

    \int e^xsin2xdx=sin 2x e^x - \frac{1}{2} cos 2x e^x +\frac{1}{4}\int e^xsin2x dx
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Aug 2009
    Posts
    71
    You actually can continue. For example consider the following:
    <br />
y = 5x^2 + 3y
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328
    Quote Originally Posted by dandaman View Post
    k thanks for the response I got -pi/4 for #1
    but for #2, i cant get the answer.
    this is what i get and can't continue from here.

    \int e^xsin2xdx=sin 2x e^x - \frac{1}{2} cos 2x e^x +\frac{1}{4}\int e^xsin2x dx
    That is A= B- C+ (1/4)A. Can you solve that for A?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2012, 02:30 PM
  2. Replies: 8
    Last Post: September 2nd 2010, 12:27 PM
  3. Replies: 0
    Last Post: April 23rd 2010, 03:01 PM
  4. Replies: 1
    Last Post: February 17th 2009, 06:55 AM
  5. Help with Integration by Parts Problems
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2008, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum