   Chapter 6.1, Problem 7SWU ### 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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# In Exercises 7-10, find the area of the region bounded by the graphs of f and g. f ( x ) = − x 2 + 4 ,    g ( x ) = x 2 − 4

To determine

To calculate: The area of the region bounded by the graphs of f(x)=x2+4 and g(x)=x24.

Explanation

Given Information:

The functions f(x)=x2+4 and g(x)=x24.

Formula used:

The equation of the parabola (yk)=(xh)2 opening downwards with vertex (h,k).

The equation of the parabola (yk)=(xh)2 opening upwards with vertex (h,k).

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:

Consider the function, f(x)=x2+4

Let y=f(x)

y=x2+4y4=x2

Comparing it with the equation of the parabola (yk)=(xh)2 opening downwards with vertex (h,k).

The given function represents a parabola opening downwards with vertex (0,4)

So, its graph appears as follows:

Consider the second function, g(x)=x24

Let y=g(x)

y=x24y+4=x2

Comparing it with the equation of the parabola (yk)=(xh)2 opening upwards with vertex (h,k)

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