Results 1 to 5 of 5

Math Help - Integrate Multivariable Function using polar co-ords

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    28

    Integrate Multivariable Function using polar co-ords

    Hello,

    Trying to solve this,

    \int_a^b{\int_c^d{\cos(x^2+y^2)\,dx}\, dy}

    Over the reigon A, where A is

    x>=0, y>=0, x^2+y^2 <= \frac{pi}{2}

    I've attempted to work out initially what the limits a,b,c,d are. Would I be correct in thinking these were 0, sqrt(pi/2), 0, sqrt(pi/2)?

    Then I'm struggling to convert these limits into polar form.

    Thank you!
    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
    45

    Re: Integrate Multivariable Function using polar co-ords

    We have:

    A \equiv \begin{Bmatrix} 0\leq x\leq \sqrt{\pi/2}\\0\leq y\leq \sqrt{\pi/2-x^2}\end{matrix} \equiv \begin{Bmatrix} 0 \leq \theta\leq \pi/2\\0\leq \rho\leq \sqrt{\pi/2}\end{matrix}

    So, the integral is I=\int_0^{\pi/2}d\theta\int_0^{\sqrt{\pi/2}} \rho\;(\cos \rho^2)\;d\rho
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2010
    Posts
    28

    Re: Integrate Multivariable Function using polar co-ords

    Thanks for the response, could you please explain why

    Quote Originally Posted by FernandoRevilla View Post
    0\leq y\leq \sqrt{\pi/2-x^2}
    ?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Integrate Multivariable Function using polar co-ords

    Sketch the quarter of circle: fixing x\in [0,\sqrt{\pi/2}] , y varies from 0 to \sqrt{\pi/2-x^2} .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,449
    Thanks
    1864

    Re: Integrate Multivariable Function using polar co-ords

    Quote Originally Posted by MattWT View Post
    Hello,

    Trying to solve this,

    \int_a^b{\int_c^d{\cos(x^2+y^2)\,dx}\, dy}

    Over the reigon A, where A is

    x>=0, y>=0, x^2+y^2 <= \frac{pi}{2}

    I've attempted to work out initially what the limits a,b,c,d are. Would I be correct in thinking these were 0, sqrt(pi/2), 0, sqrt(pi/2)?

    Then I'm struggling to convert these limits into polar form.

    Thank you!
    You have an integral of the form \int_a^b\int_c^d f(x,y)dxdy only if the region of integration is a rectangle!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Double integrals with polar co-ords
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 10th 2011, 02:53 AM
  2. Replies: 11
    Last Post: February 21st 2011, 10:35 AM
  3. Area integral in polar co-ords of a surface
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 18th 2010, 04:48 AM
  4. Replies: 8
    Last Post: May 6th 2009, 01:21 PM
  5. Vector Calculus in Spherical Polar Co-ords.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 26th 2008, 10:18 AM

Search Tags


/mathhelpforum @mathhelpforum