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Math Help - double integral

  1. #1
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    double integral

    any help would much be appreciated!

    Find the area of the region enclosed by the ellipse x^2/a^2 + y^2/b^2 =1
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  2. #2
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    Let R=\left\{ (x,y)\in \mathbb{R}^{2}\bigg|\frac{x^{2}}{a^{2}}+\frac{y^{2  }}{b^{2}}\le 1,\,a,b>0 \right\}.

    Put (u,v)=\left( \frac{x}{a},\frac{y}{b} \right), whereat du\,dv=\frac{dx\,dy}{ab} and the region R will be transfered to the unit circle u^{2}+v^{2}\le 1.

    Switch to polar coordinates and we're done.
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  3. #3
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    I don't understand could you please explain more.
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  4. #4
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    Unless you don't tell what's exactly you don't understand, I can't help further.
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  5. #5
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    ok I do get it now, but then i'm stuck i get
    and the Jacobian is and so then



    what do i do now, can you please help me finish this off
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  6. #6
    MHF Contributor matheagle's Avatar
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    You can swich to polar to integrate this.
    BUT as the previous poster said, it's now a circle with radius one.
    Thus the area inside of it is PI.
    Hence, there's no need to integrate.
    Giving you ab\pi as the answer.
    This works in all dimensions.
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  7. #7
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    switching to polar what would we get
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  8. #8
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by sonia1 View Post
    switching to polar what would we get

    There is no reason to integrate.
    The area of a circle with radius one is \pi.
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  9. #9
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    but we've been asked to use double integration
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