Explanation Given information: Consider the integral ∫ ∫ R ( 1 − x ) d A , R = [ 0 , 2 ] × [ − 7 , 7 ] . Formula used: The formula of the integral is: ∫ ∫ R ( f ( x , y ) + g ( x , y ) ) d A = ∫ ∫ R f ( x , y ) d A + ∫ ∫ R g ( x , y ) d A Calculation: Rewrite the integral is: ∫ ∫ R ( 1 − x ) d A = ∫ ∫ R 1 d A − ∫ ∫ R x d A The function is f ( x , y ) = ( 1 − x ) . Now, f ( x , y ) takes opposite values at ( x , y ) and ( x , − y )

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ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 15.1, Problem 16E

To determine

Find the double integral ∫∫R(1−x) dA,R=[0,2]×[−7,7], using symmetry.

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Chapter 15.1, Problem 15E

Chapter 15.1, Problem 17E

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Chapter 15 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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Find the double integral ∫ ∫ R ( 1 − x ) d A , R = [ 0 , 2 ] × [ − 7 , 7 ] , using symmetry.

Solution Summary: The author explains how to rewrite the integral using symmetry. The function f(x,y) takes opposite values.

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Find the double integral ∫∫R(1−x) dA,R=[0,2]×[−7,7], using symmetry.

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Chapter 15 Solutions