Explanation Given information: The base of a solid is the region bounded by parabolas y = x 2 and y = 2 − x 2 . Calculation: Show the Equations of parabola as follows: y = x 2 (1) y = 2 − x 2 (2) Equate Equation (1) and (2). x 2 = 2 − x 2 2 − x 2 − x 2 = 0 Solve the equation. x 2 = 2 − x 2 2 x 2 = 2 x 2 = 1 x = ± 1 Hence, the limits of the region bounded by the curves is [ − 1 , 1 ] . Find the volume of the region using the formula: V = ∫ a b A ( x ) d x (3) Substitute − 1 for a , 1 for b , and ( 2 − x 2 − x 2 ) for A ( x ) in Equation (3). V = ∫ − 1 1 [ ( 2 − x 2 ) − x 2 ] d x (4) The region bounded by the curve is symmetrical about the x axis

Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)

8th Edition

ISBN: 9781305272422

Author: James Stewart, Jeffrey A. Cole, Daniel Drucker, Daniel Anderson

Publisher: Cengage Learning

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Chapter 6, Problem 24RE

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To find: the volume of the solid if cross section perpendicular to the x axis.

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Chapter 6, Problem 23RE

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Chapter 6 Solutions

Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)

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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the volume of the solid if cross section perpendicular to the x axis.

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Chapter 6 Solutions