   Chapter 8.5, Problem 53E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding the Area of a Region In Exercises 53-56, sketch the region bounded by the graphs of the functions and find the area of the region. y = cos   x ,   y   = 2 − cos   x ,   x = 0 ,   x = 2 π

To determine

To graph: The region bounded by the functions, y=cosx and y=2cosx for x=0 to x=2π and also calculate the area of the region.

Explanation

Given Information:

The provided functions are y=cosx and y=2cosx for x=0 to x=2π.

Formula used:

The formula of definite integral of abcosudu.

abcosudu=[sinu]ab

Here, n is the any positive integer.

The formula of definite integral of abdu.

abdu=[u]ab

Graph:

For the region bounded by graph of y=cosx and y=2cosx for x=0 to x=2π.

Consider the provided function.

y=cosx

At x=0,

yx=0=cos0=1

At x=π2,

yx=π2=cosπ2=0

At x=π,

yx=π=cosπ=1

At x=3π2,

yx=3π2=cos3π2=0

At x=2π,

yx=2π=cos2π=1

Now, the table for ordered pair (x,y) for the function y=cosx is shown below,

xy01π/20π13π/202π1

Now also, consider the provided function.

y=2cosx

At x=0,

yx=0=2cos0=21=1

At x=π2,

yx=π2=2cosπ2=20=2

At x=π,

yx=π=2cosπ=2(1)=3

At x=3π2,

yx=3π2=2cos3π2

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