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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the area of the shaded region.

Chapter 6.1, Problem 2E, Find the area of the shaded region.

To determine

The area of the given shaded region.

Explanation

Given information:

The upper bound curve y=f(x) is 2x.

The lower bound curve y=g(x) is x24x.

The shaded region lies between x=0 and x=6. Hence, the limits are a=0 and b=6.

Calculation:

Calculate the area of the shaded region using the area formula.

A=abf(x)dxabg(x)dx (1)

Here, the area of region bounded by the upper curve is abf(x)dx and the area of region bounded by lower curve is abg(x)dx.

Substitute 2x for f(x), x24x for g(x), 0 for a, and 6 for b in Equation (1)

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