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Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √7x from 0 to 28. Solution This problem can be solved using disks. To use shells we relabel the curve y = √7x as x = y shell height = 28-y²/7 y x = y²/7 x = 28 shell radius = y 28 For rotation about the x-axis we see that a typical shell has radius y, circumference 2лy, and height . So the volume is 14 V = S ["¹" (2xY) (28 - 12/1²) dy = (¹^ (28y - 1/1/1³) dy 114 = 2π 2x [ = 0 In this problem the disk method is simpler. 14 y²/7 i dy = 2π

Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √7x from 0 to 28. Solution This problem can be solved using disks. To use shells we relabel the curve y = √7x as x = y shell height = 28-y²/7 y x = y²/7 x = 28 shell radius = y 28 For rotation about the x-axis we see that a typical shell has radius y, circumference 2лy, and height . So the volume is 14 V = S ["¹" (2xY) (28 - 12/1²) dy = (¹^ (28y - 1/1/1³) dy 114 = 2π 2x [ = 0 In this problem the disk method is simpler. 14 y²/7 i dy = 2π

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √7x from 0 to 28. Solution This problem can be solved using disks. To use shells we relabel the curve y = √7x as x = || YA shell height = 28 - y²/7 14 y f x = y²/7 X = 28 shell radius = y Xx 28 For rotation about the x-axis we see that a typical shell has radius y, circumference 2лy, and height . So the volume is 14 14 V = = [¹ ^ (2xy) (28 - 1²- y²) dy = 2x · 2x ['¹^ (28Y - 1/1 1²³) dy -y- /0 114 = 2π []*-| = 0 In this problem the disk method is simpler. y²/7
Transcribed Image Text:Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √7x from 0 to 28. Solution This problem can be solved using disks. To use shells we relabel the curve y = √7x as x = || YA shell height = 28 - y²/7 14 y f x = y²/7 X = 28 shell radius = y Xx 28 For rotation about the x-axis we see that a typical shell has radius y, circumference 2лy, and height . So the volume is 14 14 V = = [¹ ^ (2xy) (28 - 1²- y²) dy = 2x · 2x ['¹^ (28Y - 1/1 1²³) dy -y- /0 114 = 2π []*-| = 0 In this problem the disk method is simpler. y²/7
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