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Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636

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BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636
Chapter 5.1, Problem 2E
Textbook Problem
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Find the area of the shaded region.

Chapter 5.1, Problem 2E, Find the area of the shaded region.

To determine

To find: The area of the given shaded region.

Explanation of Solution

Given:

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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Chapter 5 Solutions

Single Variable Calculus
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Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - The graphs of two functions are shown with the...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Sketch the region enclosed by the given curves and...Ch. 5.1 - Use calculus to find the area of the triangle with...Ch. 5.1 - Use calculus to find the area of the triangle with...Ch. 5.1 - Evaluate the integral and interpret it as the area...Ch. 5.1 - Evaluate the integral and interpret it as the area...Ch. 5.1 - Use a graph to find approximate x-coordinates of...Ch. 5.1 - Use a graph to find approximate x-coordinates of...Ch. 5.1 - Use a graph to find approximate x-coordinates of...Ch. 5.1 - Use a graph to find approximate x-coordinates of...Ch. 5.1 - Graph the region between the curves and use your...Ch. 5.1 - Graph the region between the curves and use your...Ch. 5.1 - Graph the region between the curves and use your...Ch. 5.1 - Graph the region between the curves and use your...Ch. 5.1 - Use a computer algebra system to find the exact...Ch. 5.1 - Sketch the region in the xy-plane defined by the...Ch. 5.1 - Racing cars driven by Chris and Kelly are side by...Ch. 5.1 - The widths (in meters) of a kidney-shaped swimming...Ch. 5.1 - A cross-section of an airplane wing is shown....Ch. 5.1 - If the birth rate of a population is b(t) = 2200 +...Ch. 5.1 - In Example 5, we modeled a measles pathogenesis...Ch. 5.1 - The rates at which rain fell, in inches per hour,...Ch. 5.1 - Two cars, A and B, start side by side and...Ch. 5.1 - The figure shows graphs of the marginal revenue...Ch. 5.1 - The curve with equation y2 = x2(x + 3) is called...Ch. 5.1 - Find the area of the region bounded by the...Ch. 5.1 - Find the number b such that the line y = b divides...Ch. 5.1 - (a) Find the number a such that the line x = a...Ch. 5.1 - Find the values of c such that the area of the...Ch. 5.1 - Suppose that 0 c /2. 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(b)...Ch. 5 - Suppose that you push a book across a 6-meter-long...Ch. 5 - (a) What is the average value of a function f on...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the area of the region bounded by the given...Ch. 5 - Find the volume of the solid obtained by rotating...Ch. 5 - Find the volume of the solid obtained by rotating...Ch. 5 - Find the volume of the solid obtained by rotating...Ch. 5 - Find the volume of the solid obtained by rotating...Ch. 5 - Find the volume of the solid obtained by rotating...Ch. 5 - Set up, but do not evaluate, an integral for the...Ch. 5 - Set up, but do not evaluate, an integral for the...Ch. 5 - Set up, but do not evaluate, an integral for the...Ch. 5 - Find the volumes of the solids obtained by...Ch. 5 - Let R be the region in the first quadrant bounded...Ch. 5 - Let R be the region bounded by the curves y =...Ch. 5 - Let R be the region bounded by the curves y = 1 ...Ch. 5 - Each integral represents the volume of a solid....Ch. 5 - Each integral represents the volume of a solid....Ch. 5 - Each integral represents the volume of a solid....Ch. 5 - Each integral represents the volume of a solid....Ch. 5 - The base of a solid is a circular disk with radius...Ch. 5 - The base of a solid is the region bounded by the...Ch. 5 - The height of a monument is 20 m. 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