Results 1 to 2 of 2

Math Help - Apply Green's Theorem to evaluate the integral

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    295
    Thanks
    9

    Apply Green's Theorem to evaluate the integral

    \displaystyle \oint_{C}4ydx+2ydy

    Where C: 0\leq x\leq \pi, 0\leq y \leq sin(x)

    Ok, so I let M=4y and N=2y

    And then

    \displaystyle \iint_{R} \frac{\partial N}{\partial x}-\frac{\partial M}{\partial Y}dxdy

    Comes out to

    \displaystyle \int_{0}^{\pi}\int_{0}^{sin(x)} -4dydx

    Then

    \displaystyle \int_{0}^{\pi}[-4y|^{sin(x)}_{0}]dx

    Which gives me

    \displaystyle \int_{0}^{\pi}-4sin(x)dx

    \displaystyle 4cos(x)|^{\pi}_{0}

    Which is

    -4-4=-8

    The answer in the book, however, is -4. What am I doing wrong? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44
    Quote Originally Posted by downthesun01 View Post
    The answer in the book, however, is -4. What am I doing wrong? Thanks
    Nothing, your book is wrong. The answer is -8 .

    Regards.

    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Green's Theorem to evaluate an integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2009, 09:40 PM
  2. Line Integral and Green's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 4th 2009, 07:25 PM
  3. Green's Theorem Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 4th 2009, 08:59 AM
  4. Replies: 4
    Last Post: March 10th 2009, 05:32 PM
  5. Replies: 1
    Last Post: December 25th 2008, 06:15 AM

/mathhelpforum @mathhelpforum