   Chapter 8.3, Problem 73E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The area of given regionbounded by the followingequations, y=cos2x , y=sin2x Explanation

Given:

The givenequations y=cos2x , y=sin2x which depicted by the following graph

Formula Used:

The function representing the curve is integrated on the points between which the curve lies to find the area.

abf(x)dx

Calculation:

Consider following equations which bound the given region,

y=cos2x , y=sin2x

In the graph, shaded region lies between π4 to π4,

Therefore, the limit of x,

x=π4 , π4

We can calculate area of region with definite integral as,

A=π4π4(cos2xsin2x)dx

By using the trigonometry identity,

cos2x=cos2xsin2x

To get,

A=

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