   Chapter 5.5, Problem 15E ### 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   =   x 2 −   1 ,   y   =   − x +   2 , x =   0 , x   = 1

To determine

To graph: The region bounded by the graphs of y=x21, y=x+2, x=0 and x=1, and also compute the area of the region.

Explanation

Given Information:

The region bounded by the graphs of y=x21, y=x+2, x=0 and x=1.

Graph:

Consider the provided functions,

y=x21

And, y=x+2

Consider the first function y=x21

It is a quadratic function. So, its graph will be a parabola with opening upwards. Compute its x-intercepts as follows:,

x21=0x2=1x=±1

The x-intercepts are x=±1.

Consider the second function y=x+2

It is a linear function. So, its graph will be a straight line with slope m=1 and y-intercept b=2

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

Calculation:

From the graph, (x21)(x+2) for all x in the interval [0,1]

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