Explanation Given information: The two curves has a function of x = y 4 and y = 2 − x . The lower limit is 0. Calculation: Find the intersection points of the curves by equating the curves as shown below: f ( y ) = g ( y ) (1) Here, the right curve function is f ( y ) and the left curve function is g ( y ) . Rearrange the curve function y = 2 − x as shown below: y 2 = 2 − x x = 2 − y 2 Substitute 2 − y 2 for f ( y ) and y 4 for g ( y ) in Equation (1). 2 − y 2 = y 4 y 4 + y 2 − 2 = 0 ( y 2 + 2 ) ( y 2 − 1 ) = 0 (2) Consider the positive value of y as the limit in Equation (2), since y ≥ 0 . y 2 = 1 y = 1 Procedure to sketch the region bounded by the two curves is explained below: Draw the graph for the function x = y 4 by substituting different values for y . Similarly in the same graph plot for the function y = 2 − x by substituting different values for y . Shade the region lies between y = 0 and y = 1 . The region enclosed by the curves x = y 4 and y = 2 − x is shown in Figure 1

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

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Chapter 6.1, Problem 20E

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 19E

Chapter 6.1, Problem 21E

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Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.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 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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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 the procedure to sketch the region bounded by the two curves.