# Evaluate \iiint_{E} 8(x^{3} + xy^{2}) dV, where E is the solid in the first octant that lies...

## Question:

Evaluate {eq}\displaystyle\;\iiint_{E} 8\left(x^{3} + xy^{2}\right) dV, \; {/eq} where {eq}\,E\, {/eq} is the solid in the first octant that lies beneath the paraboloid {eq}\,z = 4 - x^{2} - y^{2} {/eq}.

## Multiple Integral:

An integral that has more than one variable is known as multiple integral. Here, we are given a triple integral ( an integral that contains three variables) of the form {eq}\iiint f(x,y,z) dV {/eq} and we have to evaluate it. To compute this, we 'll apply cylindrical coordinates which is an extension of polar coordinates.

## Answer and Explanation: 1

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We have to evaluate {eq}\displaystyle\;\iiint_{E} 8\left(x^{3} + xy^{2}\right) dV, \; {/eq} where {eq}\,E\, {/eq} is the solid in the first...

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