Calculate the integral of the function f (x, y, z) = xyz on the region bounded...

Calculate the integral of the function f (x, y, z) = xyz on the region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^ 2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.

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Expert Solution

The lower bound of the region over which we are to integrate is z=3 at he bottom.

But, the upper bound is given to be the cylinder x²+y²=1 that is actually unbounded above.

Again the bound from the sides is given to be the paraboloid x²+y²+4. The minima of this surface is (0,0,4) Then the lower bound to be z=3 does not make any sence.

THE LIMIT OF THE TRIPLE INTEGRATION NAMELY D IS :-

Z=3 from bottom , x²+y²=1 for the sides , x²+y²+4 at the top.

We use cylindrical coordinates for this integral.

The answer is 0.

Colby Messinger answered 1 year ago

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