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Math Help - calculus help!!!

  1. #1
    Newbie
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    calculus help!!!

    Hi,

    1.) Let R be the region in the xy plane that is outside the circle x^2+y^2=1 but inside the circle x^2+y^2=2 . Evaluate the double integral

    double integration over R {1/x^2+y^2}dA

    2.) Evaluate the integrals
    double integrals
    integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)

    sorry if it is difficult to understand in written pattern.

    I will appreciate if any can help me and thanks again
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
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    Hi,
    Quote Originally Posted by Mr.Green View Post
    1.) Let R be the region in the xy plane that is outside the circle x^2+y^2=1 but inside the circle x^2+y^2=2 . Evaluate the double integral

    double integration over R {1/x^2+y^2}dA

    2.) Evaluate the integrals
    double integrals
    integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)
    You should try switching to polar coordinates.
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Santiago, Chile
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    Quote Originally Posted by Mr.Green View Post

    2.) integral 0 to infinite integral 0 to infinite {dydx/(1+x^2+y^2)^3/2)
    Following up on flyingsquirrel's suggestion, we have that x,y are taken in the first quadrant, hence 0\le r<\infty,\,0\le\varphi\le\frac\pi2 and the double integral becomes \int_{0}^{\pi /2}{\int_{0}^{\infty }{\frac{r}{\left( 1+r^{2} \right)^{3/2}}\,dr}\,d\varphi }=\frac{\pi }{2}.
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