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Thread: Need help solving this integral

  1. #1
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    Need help solving this integral

    Hi!

    The problem says:

    A region R in the plane consists of those points (x,y) which satisfy the inequalities

    1_<x^2+y^2<_4
    0_<x
    0_<y

    And the intgral is
    SSR (x^2+y^2-1)dA

    (a screenshot of the problem is attached)

    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Need help solving this integral-problem-10.jpg  
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  2. #2
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    Re: Need help solving this integral

    Convert to polar coordinates. This gives you $1\le r \le 2$ and $0 \le \theta \le \dfrac{\pi}{2}$.

    $\displaystyle \int_0^{\tfrac{\pi}{2}} \int_1^2 (r^2-1)r{dr}{d\theta} = \int_0^{\tfrac{\pi}{2}}\dfrac{9}{4}{d\theta} = \dfrac{9\pi}{8}$
    Thanks from HallsofIvy and MarceloFF
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  3. #3
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    Re: Need help solving this integral

    Hi.

    Why is (r^2−1) multiplied by r?

    Thank you very much for your answer!

    Oh okay, dA = rdrd0, sorry
    Last edited by MarceloFF; Jun 10th 2017 at 07:04 AM.
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