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siddharth

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The question is, Find the volume of the region bounded by the hyperboloid cylinders

[tex] xy=1, xy=9, xz=36, yz=25, yz=49 [/tex]

The Volume will be

[tex] \int \int \int_{V} dx dy dz [/tex]

which I think is,

[tex] \int \int_{D} (\frac{49}{y}-\frac{25}{y})dx dy [/tex]

The problem I now have is in determining the Domain of Integration D in the x-y plane. I know I am supposed to project the cylinder on to the x-y plane and then find the domain D, but I am stuck. How do I find the curves, y=f(x), which determines this domain?

[tex] xy=1, xy=9, xz=36, yz=25, yz=49 [/tex]

The Volume will be

[tex] \int \int \int_{V} dx dy dz [/tex]

which I think is,

[tex] \int \int_{D} (\frac{49}{y}-\frac{25}{y})dx dy [/tex]

The problem I now have is in determining the Domain of Integration D in the x-y plane. I know I am supposed to project the cylinder on to the x-y plane and then find the domain D, but I am stuck. How do I find the curves, y=f(x), which determines this domain?

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