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Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral.

0π02π05p2sinϕdpdθdϕ

Short Answer

Expert verified

0π02π05p2sinϕdpdθdϕ=5003π

Step by step solution

01

Given

We have to find the volume by using the triple integral.

0π02π05p2sinϕdpdθdϕ
02

Evaluate integral

V=0π02π05p2sinϕdpdθdϕV=0πsinϕdϕ02πdθ05p2dpV=p33050πsinϕdϕ02πdθV=12530πsinϕdϕ02πdθV=1253(2π)0πsinϕdϕV=2503π-cosϕ0πV=2503π1+1V=5003πcubicunits

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