10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

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 = tan x , y = 0 , x = − π 4 , x = π 4

To determine

To calculate: The volume of the solid generated by revolving the region bounded by the graphs of the provided equations about x−axis.

Given: The following equations;

y=tanx , y=0 , x=−π4 , x=π4

Formula Used:

The volume is calculated by the following formula;

The following trigonometric identity;

tan2x=sec2x−1

The following integral formula;

∫sec2udu=tanu+C

Calculation:

First consider the equations forming the region,

y=tanx , y=0 , x=−π4 , x=π4

From the graph, it is clear that the shaded region lies between −π4 to π4,

Now the limit of x are,

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

Check out a sample textbook solution.

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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 = tan x , y = 0 , x = − π 4 , x = π 4

Chapter 8 Solutions

Additional Math Solutions

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Calculus

Solutions

Calculus

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 = tan x , y = 0 , x = − π 4 , x = π 4

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Calculus Calculus 10th Edition

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 = tan x , y = 0 , x = − π 4 , x = π 4