Explanation Given information: The two curves has a function of y = cos π x and y = 4 x 2 − 1 . Procedure to sketch the region bounded by the two curves is explained below: Draw the graph for the function y = cos π x by substituting different values for x . Similarly in the same graph plot for the function y = 4 x 2 − 1 by substituting different values for x . Shade the region lies between the intersecting points of the curves. The region enclosed by the curves y = cos π x and y = 4 x 2 − 1 is shown in Figure 1. Refer to Figure 1. The two curves intersects at x = − 1 2 and x = 1 2 The curves are bounded by the top and bottom curve. Hence, the integration can be done with respect to x . Calculation: Find the area of the region bounded by the curves using the relation: A = ∫ a b ( f ( x ) − g ( x ) ) d x (1) Here, the top curve is f ( x ) , the bottom curve is g ( x ) , the lower limit is a , and the upper limit is b . Substitute cos π x for f ( x ) , 4 x 2 − 1 for g ( x ) , − 1 2 for a , and 1 2 for b in Equation (1)

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Question

Chapter 6.1, Problem 19E

To determine

To draw: The region enclosed by the given curves.

The area of the region enclosed by the curves.

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Chapter 6.1, Problem 18E

Chapter 6.1, Problem 20E

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Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....

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To draw: The region enclosed by the given curves. The area of the region enclosed by the curves.

Solution Summary: The author explains how to draw the region enclosed by the curves using the function y=mathrmcospi x.