Results 1 to 3 of 3

Math Help - Integration by Parts

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    158

    Integration by Parts

    integrate integral from 0 to t of e^s sin(t-s)ds.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member ursa's Avatar
    Joined
    Jan 2009
    From
    Delhi
    Posts
    60
    integrate integral from 0 to t of e^s sin(t-s)ds.
    hi
    Simply apply the by parts rule, you will get the answer
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Integration by Parts

    Hello twilightstr
    Quote Originally Posted by twilightstr View Post
    integrate integral from 0 to t of e^s sin(t-s)ds.
    This is one of these integration by parts questions where you integrate by parts twice, and this brings you back to the integral you started with (plus some other bits as well). If you call the original integral I, you can then put I back into the equation and then solve the resulting equation for I.

    Here's the first bit:

    I = \int_0^t e^s \sin(t-s)ds = [e^s \cos(t-s)]_0^t - \int_0^te^s \cos(t-s)ds

    Is that OK? I've integrated \sin(t-s) to get \cos(t-s), and differentiated e^s to get e^s.

    Now use Parts again on the second integral, and you'll find you get back to the integral you started with. Put this equal to I, and solve.

    See if you can complete it now.

    Grandad
    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. Integration by Parts!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 22nd 2010, 03:19 AM
  5. Replies: 1
    Last Post: February 17th 2009, 06:55 AM

Search Tags


/mathhelpforum @mathhelpforum