Explanation Given: In the integral ∫ 0 a ∫ 0 b e max { b 2 x 2 , a 2 y 2 } d y d x , limits a and b are positive. Formula used: Calculation: Assume I = ∫ 0 a ∫ 0 b e max { b 2 x 2 , a 2 y 2 } d y d x . Divide the rectangle into two parts by the diagonal a y = b x . In the lower triangle, b 2 x 2 ≥ a 2 y 2 because y ≤ b a x . For the lower triangle, Limits of x lie from 0 to 1 and limits of y lie from 0 to b a x . Similarly, For the upper triangle, The limits of y lie from 0 to 1 and limits of x lie from 0 to a b y . The value of the integral is calculated by adding the integral on both the triangles. The value of the integral is: I = ∫ 0 a ∫ 0 b x a e b 2 x 2 d y d x + ∫ 0 b ∫ 0 a y b e a 2 y 2 d x d y

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.2, Problem 75E

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To calculate: The value of the integral ∫0a∫0bemax{b2x2,a2y2}dydx.

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Chapter 14.2, Problem 74E

Chapter 14.2, Problem 76E

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The value of the integral ∫ 0 a ∫ 0 b e max { b 2 x 2 , a 2 y 2 } d y d x .

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To calculate: The value of the integral ∫0a∫0bemax{b2x2,a2y2}dydx.

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Chapter 14 Solutions