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adoni [48]
3 years ago
8

Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate​ planes, usi

ng triple integrals.
Mathematics
1 answer:
dem82 [27]3 years ago
3 0

First,

9x+15y+15z=45\implies 3x+5y+5z=15

The volume is given by the integral (one of 6 possible combinations),

\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}

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