   Chapter 5.5, Problem 19E ### 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 Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4. y = 1 x 2 , y = 0 , x = 1 , x = 5

To determine

To graph: The region bounded by the graphs of y=1x2, y=0, x=1 and x=5, and also compute the area of the region.

Explanation

Given Information:

The region bounded by the graphs of y=1x2, y=0, x=1 and x=5.

Graph:

Consider the provided functions,

y=1x2

And, y=0

Then the first function is y=1x2

Compute the x-intercepts as follows:

1x2=0x2=10

It is not possible, so there is no x-intercept and no y-intercept. The graph of the function will lie only in first and second quadrants. As x increases in both directions, y will decrease.

Consider the second function y=0

It is the equation of x-axis.

Compute the points of intersection of two graphs by setting the functions equal to each other and solving for x,

1x2=0x2=10

To find the intersection points between x=1 and y=1x2.

y=1x2=1

And

To find the intersection points between x=5 and y=1x2.

y=1x2=125=0.04

Sketch the graph of two functions as follows:

Formula used:

Area of a region bounded by two graphs is calculated using the following formula,

If f and g are continuous on [a,b] and g(x)f(x) for all x in [a,b], then the area of the region bounded by the graphs of f, g, x=a and x=b is given by

A=ab[f(x)g(x)]dx

The integral of xndx=xn+1n+1+C

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