Results 1 to 2 of 2

Thread: 232.q1.5c evaluate dbl int

  1. #1
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    634

    232.q1.5c evaluate dbl int

    Evaluate:$$\int_{0}^{1} \int_{\sin^{-1}{y}}^{\frac{\pi}{2}}
    \cos{x}\sqrt{1+\cos^2{x}}
    \,dx \,dy$$
    my first inclination is $u=1+\cos^2{x}$ but ???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,680
    Thanks
    2389

    Re: 232.q1.5c evaluate dbl int

    let $u=\sin(x)$

    $du=\cos(x)~dx$

    Note that $1+\cos^2(x) = 2 - \sin^2(x)$

    $\displaystyle \int_0^1 \int_y^1 \sqrt{2-u^2}~du~dy =$

    $\displaystyle \int_0^1 \dfrac{1}{4} \left(-2 \sqrt{2-y^2} y-4 \sin ^{-1}\left(\dfrac{y}{\sqrt{2}}\right)+\pi +2\right)~dy =$

    $\dfrac{1}{3} \left(2 \sqrt{2}-1\right)$

    I leave it to you to figure out that first integration over $u$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Evaluate.
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Sep 6th 2012, 04:13 PM
  2. [SOLVED] Evaluate b_{n}
    Posted in the Calculus Forum
    Replies: 11
    Last Post: Feb 23rd 2011, 05:36 PM
  3. [SOLVED] Evaluate (A+1)(A-I)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Feb 19th 2011, 07:07 AM
  4. evaluate
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Nov 21st 2009, 03:26 AM
  5. evaluate
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Dec 11th 2007, 04:54 AM

/mathhelpforum @mathhelpforum