(a) Explanation Given information: The region is denoted as ℜ . The region bounded by the curves y = tan ( x 2 ) , x = 1 and y = 0 . The midpoint Rule with number of subintervals as n = 4 Calculation: The region bounded by the curves is shown below: y = tan ( x 2 ) (1) Calculate the area using the function as follows: A = ∫ a b [ f ( x ) ] d x Substitute 0 for a , 1 for b , and tan ( x 2 ) for [ f ( x ) ] in Equation (2). A = ∫ 0 1 tan x 2 d x (2) Calculate the volume using the midpoint rule with n = 4 : Consider f ( x ) = tan ( x ) 2 (3) Substitute f ( x ) for tan ( x 2 ) in Equation (2). A = ∫ 0 1 f ( x ) d x = 1 − 0 4 [ f ( 0.125 ) + f ( 0.375 ) + f ( 0.625 ) + f ( 0.875 ) ] = 1 4 [ f ( 0.125 ) + f ( 0 (b) To determine To find : The volume obtained by rotating region about x -axis.

9th Edition

ISBN: 9780357128923

Author: Stewart

Publisher: CENGAGE L

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Question

Chapter 6, Problem 19E

(a)

To determine

To calculate:

(b)

To determine

To find: The volume obtained by rotating region about x-axis.

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Chapter 6 Solutions

CALCULUS,EARLY TRANS.-WEBASSIGN ACCESS

Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - (a) Set up an integral for the area of the shaded...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. 5.Ch. 6.1 - Find the area of the shaded region. 6.Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Prob. 8E Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Set up, but do not evaluate, an integral...

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