Results 1 to 2 of 2

Math Help - triple integration

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    57

    triple integration

    Can anyone help plzzzz...

    \int_{0}^{\pi/2}\int_{0}^{\pi/2}\int_{0}^{\pi/2}\cos(x+y)*cos(y+z)dxdydz
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by sonia1 View Post
    Can anyone help plzzzz...

    \int_{0}^{\pi/2}\int_{0}^{\pi/2}\int_{0}^{\pi/2}\cos(x+y)*cos(y+z)dx dydz

    Since we are integrating over a rectangle Fubini's theorem tells us the order of the interated integrals does not matter.

    first w.r.t x we get

    \int_{0}^{\pi/2}\cos(x+y)\cos(y+z)dx=\sin(x+y)\cos(y+z) \bigg|_{0}^{\pi /2}=

    \sin\left(\frac{\pi}{2}+y \right)\cos(y+z)-\sin(y)\cos(y+z)

    Now we need to integrate this with respect to z

    \int_{0}^{\pi/2}\sin\left(\frac{\pi}{2}+y \right)\cos(y+z)-\sin(y)\cos(y+z)dz=

    \sin\left(\frac{\pi}{2}+y \right)\sin(y+z)-\sin(y)\sin(y+z) \bigg|_{0}^{\pi/2}=

    \sin^{2}\left(\frac{\pi}{2}+y \right)-\sin(y)\sin\left(y+\frac{\pi}{2}\right)-\left[ \sin\left(\frac{\pi}{2}+y \right)\sin(y)-\sin(y)\sin(y)\right]

    Now finally we only have the integral w.r.t y left so we get

    \int_{0}^{\pi/2} \sin^{2}\left(\frac{\pi}{2}+y \right)-2\sin(y)\sin\left(y+\frac{\pi}{2}\right)+\sin^{2}(  y)dy

    I will leave the last integral for you just use a few trig identites.

    Good luck
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple Integration Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2010, 12:58 PM
  2. Triple Integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 5th 2010, 04:03 AM
  3. triple integration
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 8th 2009, 12:27 AM
  4. another triple integration!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 25th 2007, 11:01 AM
  5. Triple integration
    Posted in the Calculus Forum
    Replies: 13
    Last Post: August 23rd 2006, 11:23 AM

Search Tags


/mathhelpforum @mathhelpforum