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Math Help - Multiple Integration Volume

  1. #1
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    Multiple Integration Volume

    Any help greatly appreciated.

    Find the volume of the solid under the surface z=(8+x)(8+y) and above the region in the xy-plane given by (x^2)+(y^2) less than or equal to 36.
    Hint: Use polar coordinates.

    Thanks in advance.

    Mike
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by JaysFan31
    Any help greatly appreciated.

    Find the volume of the solid under the surface z=(8+x)(8+y) and above the region in the xy-plane given by (x^2)+(y^2) less than or equal to 36.
    Hint: Use polar coordinates.

    Thanks in advance.

    Mike
    In cylindrical polars we have:

    <br />
I=\int_{r=0}^6 \int_{\theta=0}^{2\pi} \int_{z=0}^{(8+r \cos(\theta))(8+r\sin(\theta)} 1\  dz\ d\theta\ r.dr =\int_{r=0}^6 \int_{\theta=0}^{2\pi} \int_{z=0}^{(8+r \cos(\theta))(8+r\sin(\theta)} r\  dz\ d\theta\ dr <br />

    Where we have used the fact that the volume element in cylindrical polars
    is r\ d\theta\ dr \ dz, and changed the order of integration to suit the problem.

    RonL
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