Explanation Given Information: The provided integral is ∫ 1 2 ∫ 1 4 x 2 f ( x , y ) d y d x . Formula used: The value of the integral ∬ R f ( x , y ) d x d y is over the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . Graph: Consider the integral ∫ 1 2 ∫ 1 4 x 2 f ( x , y ) d y d x . Since, the integration is done with respect to y first and then with respect to x. Thus, the region is considered horizontally and when the order is reversed the region is considered vertically. The upper limit for y is 4 x 2 and lower limit is 1 and upper limit of y is 2 and lower limit is 1. Thus, the region of integration is 1 ≤ x ≤ 2 and 1 ≤ y ≤ 4 x 2 . Substitute 1 for x in y = 4 x 2 . y = 4 x 2 y = 4 1 2 y = 4 Thus, the point is ( 1 , 4 ) . Substitute 1 for y in y = 4 x 2 . 1 = 4 x 2 x 2 = 4 x = 4 = ± 2 Thus, the points are ( 2 , 1 ) and ( − 2 , 1 ) . Sketch the curve y = 4 x 2 passing through ( 1 , 4 ) , ( 2 , 1 ) and ( − 2 , 1 ) and shade the region in 1 ≤ x ≤ 2

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

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Chapter 8.5, Problem 35E

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To graph: The region of integration ∫12∫14x2f(x,y)dydx then the integrate with order reversed of the integral.

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Chapter 8.5, Problem 34E

Chapter 8.5, Problem 36E

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Chapter 8 Solutions

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 6E Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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To graph: The region of integration ∫ 1 2 ∫ 1 4 x 2 f ( x , y ) d y d x then the integrate with order reversed of the integral.

Solution Summary: The author analyzes the integral with order of integration reversed.

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To graph: The region of integration ∫12∫14x2f(x,y)dydx then the integrate with order reversed of the integral.

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Chapter 8 Solutions