   Chapter 8.3, Problem 74E

Chapter
Section
Textbook Problem

# Area In Exercises 73 and 74, find the area of the region bounded by the graphs of the equations. y = cos 2 x , y = sin x cos x , x = − π 2 , x = π 4

To determine

To calculate: The area of given region of the function y=cos2x , y=sinxcosx.

Explanation

Given: y=cos2x , y=sinxcosx

Calculation:

Consider the area in the given region,

y=cos2x , y=sinxcosx

The graph lies between the region is π2 to π4.

Refer the image in the giving question.

So that the limit of x,

x=π2 , π4

Hence the area of region is

A=π2π4(cos2xsinxcosx)dx=π2π4cos2xdxπ2π412(2sinxcosx)dx=π2π4cos2xdx12π2π4(2sinxcosx)dx

Use the trigonometry identity,

cos2x=2cos2x1sin2x=2sinxcosx

So,

A=12

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