   Chapter 8.3, Problem 76E

Chapter
Section
Textbook Problem

# Volume In Exercises 75 and 76, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x -axis. y = cos x 2 ,   y = sin x 2 ,   x = 0 ,   x = π 2

To determine

To Calculate: The volume of the solid generated by revolving the region bounded by the graphs of the provided equations about xaxis.

Explanation

Given: The following equations;

y=cosx2 , y=sinx2 , x=0 ,  x=π2

Formula Used:

The volume is calculated by the following formula;

v=abπy2dx

The following trigonometric identities;

sin2x+cos2x=1sin2x=2sinxcosx

The following integral formula;

sinudu=cosu+C

Calculation:

First consider the equations forming the region,

y=cosx2 , y=sinx2 , x=0 ,  x=π2

From the graph, it is clear that the shaded region lies between 0 to π2,

Now, the limit of x is,

x=0 , π2

Hence the volume of region is calculated by the provided formula as shown below,

v=abπy2dx

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