Results 1 to 2 of 2

Math Help - definite integral

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    9

    definite integral

    evaluate the definite integral:

    I tried using substitution where U=X^8 and du=8xd^7 but I don't really know where to go with this problem



    the integral between pi/2 to -pi/2
    x8 sin x
    1 + x0
    dx


    (Sorry i couldn't figure out how to get the integral sign in)
    thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: definite integral

    If your integral is:

    I=\int\frac{x^8\sin(x)}{1+x^0}\,dx=\frac{1}{2}\int x^8\sin(x)\,dx

    then I would try integration by parts, and a bit of experience tells me we will need two formulas:

    Let:

    I_1=\int x^n\sin(x)\,dx

    u=x^n\:\therefore\:du=nx^{n-1}\,dx

    dv=\sin(x)\,dx\:\therefore\:v=-\cos(x)

    Hence:

    I_1=-x^n\cos(x)+n\int x^{n-1}\cos(x)\,dx

    Now use integration by parts again to develop a formula for the resulting integral on the right:

    I_2=\int x^n\cos(x)\,dx

    u=x^n\:\therefore\:du=nx^{n-1}\,dx

    dv=\cos(x)\,dx\:\therefore\:v=\sin(x)

    Hence:

    I_2=x^n\sin(x)-n\int x^{n-1}\sin(x)\,dx

    Now apply these formulas alternately until n-1=0 and you may evaluate the integral of a trig function alone to get the final result.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 5th 2011, 05:21 PM
  2. Replies: 4
    Last Post: April 13th 2011, 02:08 AM
  3. definite integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 19th 2010, 01:48 PM
  4. definite integral/ limit of integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2010, 04:00 AM
  5. Definite Integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 24th 2009, 06:29 AM

Search Tags


/mathhelpforum @mathhelpforum