Explanation Calculation: Use the online graphing calculator to sketch the graph of y = 1 − x , y = 1 + x , x = 4 as shown in below Figure 1. From Figure 1, it is observed that the region can be defined as R = { ( x , y ) | 1 − x ≤ y ≤ 1 + x , 0 ≤ x ≤ 4 } . Evaluate the iterated integral ∬ R x ( y − 1 ) 2 d A . First, compute the integral with respect to y . ∫ 0 4 ∫ 1 − x 1 + x x ( y − 1 ) 2 d y d x = ∫ 0 4 ∫ 1 − x 1 + x x ( y 2 − 2 y + 1 ) d y d x = ∫ 0 4 x [ ∫ 1 − x 1 + x y 2 d y − 2 ∫ 1 − x 1 + x y d y + 1 ∫ 1 − x 1 + x d y ] d x = ∫ 0 4 x [ [ y 3 3 ] 1 − x 1 + x − 2 [ y 2 2 ] 1 − x 1 + x + [ y ] 1 − x 1 + x ] d x = ∫ 0 4 x [ [ y 3 3 − y 2 + y ] 1 − x 1 + x ] d x Apply the limit value for y. ∫ 0 4 ∫ 1 − x 1 + x x ( y − 1 ) 2 d y d x d x = ∫ 0 4 x [ [ ( 1 + x ) 3 3 − ( 1 + x ) 2 + ( 1 + x ) ] − [ ( 1 − x ) 3 3 − ( 1 − x ) 2 + [ ( 1 − x ) ] ] ] d x = ∫ 0 4 x [ [ ( 1 + x ) 3 3 − ( 1 + 2 x + x ) + ( 1 + x ) ] − [ ( 1 −

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 7.7, Problem 31E

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To sketch: The graph of the given equation; and to describe the region R; then to evaluate value of the iterated integral ∬Rx(y−1)2dA.

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Chapter 7.7, Problem 30E

Chapter 7.7, Problem 32E

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Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 7.1 - Prob. 1MP Ch. 7.1 - Matched Problem 2 Find f(2, 2, 3) for f in Example...Ch. 7.1 - Prob. 3MP Ch. 7.1 - Matched Problem 4 For the box in Example 4, find...Ch. 7.1 - Matched Problem 5 Refer to Example 5. Find the...Ch. 7.1 - Matched Problem 6 Find the coordinates of the...Ch. 7.1 - Matched Problem 7 (A) Describe the cross sections...Ch. 7.1 - Explore and Discuss 1 Imagine that you are facing...Ch. 7.1 - In Problems 18, find the indicated value of the...Ch. 7.1 - Prob. 2E

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The graph of the given equation; and to describe the region R ; then to evaluate value of the iterated integral ∬ R x ( y − 1 ) 2 d A .

Solution Summary: The author explains how to sketch the graph of the given equation, and evaluate the iterated integral.

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To sketch: The graph of the given equation; and to describe the region R; then to evaluate value of the iterated integral ∬Rx(y−1)2dA.

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