(a) Explanation Given: The region bounded is y = x 2 and y = x 3 about the x-axis. Calculation: Consider the region bounded by curves of y = x 2 and y = x 3 . Using the Washer Method with volume The graph of the given region is shown as follows: V = ∫ a b π [ { f ( x ) } 2 − { g ( x ) } 2 ] d x " Outer radius will be, f ( x ) = x 2 And, the inner radius will be, g ( x ) = x 3 Compute the intersection points of two curves as follows: x 2 = x 3 x 2 − x 3 = 0 x 2 ( x − 1 ) = 0 x = 0 , 1 So, the interval for the solid line [ 0 , 1 ] Substitute, the values in the above expression f ( x ) = x 2 , g ( x ) = x 3 , a = 0 and b = 1 The volume generated will be, V (b) To determine To find: the volume generated by using shell method.

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.2, Problem 39PS

(a)

To determine

To find: the volume generated by using disk/washer method.

(b)

To determine

To find: the volume generated by using shell method.

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Chapter 6.2, Problem 38PS

Chapter 6.2, Problem 40PS

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Chapter 6 Solutions

Calculus

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the volume generated by using disk/washer method.

Solution Summary: The author calculates the volume generated by using the disk/washer method.