   Chapter 7.R, Problem 73E

Chapter
Section
Textbook Problem

# Find the area bounded by the curves y = cos x and y = cos 2 x between x = 0 and x = π .

To determine

To find:

The area bounded by the two curves between x = 0 and x = π

Explanation

Given:

The two given curves are y=cosx and y=cos2x

Formulae used:

The area enclosed by two curves f and g is given by |f(x)g(x)|dx

Consider y=cosx and the line y=cos2x between x=0 to x=π

Hence, use the method of simple integration

Now according to the given expression, the value of the area between the curves y=cosx and y=cos2x is

Graph of the curves are

The red curve is y=cosx

The blue curve is y=cos2x

From the graph

cosx is higher than cos2x for 0<x<π2

cos2x is higher than cosx for π2<x<π

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