Explanation In order to obtain the double integral, integrate the inner integral first. ∫ 0 x y x 3 e x y 2 d y = x 2 2 ∫ 0 x 3 e t d t ( t = x y 2 , then d t 2 = x y d y when y = x , t = x 3 and 0, when y = 0 ) = x 2 2 [ e t ] 0 x 3 = x 2 2 [ e x 3 − e 0 ] = x 2 2 ( e x 3 − 1 ) Now, obtain the outer integral with the help of the result of inner integral as follows

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Chapter 29.4, Problem 15E

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The value of the double integral ∫12∫0xyx3exy2dydx.

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Chapter 29.4, Problem 14E

Chapter 29.4, Problem 16E

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Chapter 29 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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The value of the double integral ∫ 1 2 ∫ 0 x y x 3 e x y 2 d y d x .

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The value of the double integral ∫12∫0xyx3exy2dydx.

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Chapter 29 Solutions