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Math Help - Polar coordinates problem

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    Polar coordinates problem

    Using polar coordinates, how to evaluate the integral where R is the region ?
    Thanks for helping!
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    Hello,
    Quote Originally Posted by iwonder View Post
    Using polar coordinates, how to evaluate the integral where R is the region ?
    Thanks for helping!
    The same way :

    x=r \cos \theta
    y=r \sin \theta

    Then 9 \leq x^2+y^2 \leq 49 can be rewritten as : 9 \leq r^2 \leq 49
    Since r is positive, this is like 3 \leq r \leq 7

    And \theta \in [0,2 \pi], in order to cover all the possibilities.

    So you have \int_0^{2 \pi} \int_3^7 \sin(r^2) ~ r ~ dr ~ d \theta

    =\left(\int_0^{2 \pi} ~ d \theta\right) \cdot \left( \int_3^7 \sin(r^2) ~ r ~ dr \right)


    make the substitution u=r^2 in the second.
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