Explanation Let there be a continuous function f ( x , y ) on R = [ a , b ] × [ c , d ] , then the below integrals are referred to as iterated integrals. ∬ R f ( x , y ) d A = ∫ a b ∫ c d f ( x , y ) d y d x = ∫ c d ∫ a b f ( x , y ) d x d y Given: A double integral as ∬ R x 3 d A , R = [ − 4 , 4 ] × [ 0 , 5 ] Formula Used: In order to compute the double integral ∬ R f ( x ) d A using symmetry, we need to check for the following points: 1. If the f ( x ) is an odd function, then ∫ − a a f ( x ) d x = 0 27. If the f ( x ) is even function, then ∫ − a a f ( x ) d x = 2 ∫ 0 a f ( x ) d x Calculation: The given problem is ∬ R x 3 d A Writing the integral as an iterated integral, we get ∬ R x 3 d A = ∫ − 4 4 ∫ 0 5 x 3 d y d x Let us first compute the indefinite integral ∫ 0 5 x 3 d y ∫ 0 5 x 3 d y = x 3 ∫ 0 2 1 d y Applying the constant rule o...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.1, Problem 15E

To determine

The value of the double integral $\iint_{R} x^{3} d A, R = [- 4, 4] \times [0, 5]$ using symmetry.

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Chapter 16.1, Problem 14E

Chapter 16.1, Problem 16E

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The value of the double integral ∬ R x 3 d A , R = [ − 4 , 4 ] × [ 0 , 5 ] using symmetry.

Solution Summary: The author explains how to compute the double integral R x 3 d A using symmetry.

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The value of the double integral $\iint_{R} x^{3} d A, R = [- 4, 4] \times [0, 5]$ using symmetry.

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Chapter 16 Solutions

The value of the double integral ∬ R x 3 d A , R = [ − 4 , 4 ] × [ 0 , 5 ] using symmetry.

Solution Summary: The author explains how to compute the double integral R x 3 d A using symmetry.

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The value of the double integral ∬Rx3dA , R = [−4,4] × [0,5] using symmetry.

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Chapter 16 Solutions

The value of the double integral $\iint_{R} x^{3} d A, R = [- 4, 4] \times [0, 5]$ using symmetry.