   Chapter 7.R, Problem 75E

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# The region under the curve y = cos 2 x , 0 ≤ x ≤ π / 2 , is rotated about the x-axis. Find the volume of the resulting solid.

To determine

To find:

The volume of the solid (generated under the given conditions).

Explanation

Given:

y=cos2x, 0<x<π2

Formulae used:

The integration dv=πy2dx

Consider y=cos2x

Use the integration to find the volume of the solid rotated about x-axis

Graph of the curve

Therefore, the volume of the disc in the region of (0,π2) is,

dV=π(cos2x)2dxV=π0π2cos4xdx=π0π2(1+cos2x)2dx=π0

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