Explanation Given : ∫ 0 1 ∫ y = x 1 x e y 3 d y d x Calculation : Step 1: The limits of integration define a vertically simple region D by the following inequalities: 0 ≤ x ≤ 1 , x ≤ y ≤ 1 . Step 2: The region can also be described as horizontally simple region by the following inequalities 0 ≤ y ≤ 1 , 0 ≤ x ≤ y Step 3: Thus, we can rewrite the given integral in reversed order of integration as follows: ∫ 0 1 ∫ y = x 1 x e y 3 d y d x = ∫ 0 1 x 2 2 e y 3 | x = 0 y d y = ∫ 0 1 e y 3 ( y 2 2 − 0 ) d y = ∫ 0 1 1 2 e y 3 y 2 d y Step 4: This integral is easy to compute using the substitution u = y 3 , d u = 3 y 2 d y ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 35E

To determine

The value of the integral $\int_{0}^{1} \int_{y = x}^{1} x e^{y^{3}} d y d x$ in reversed order of integration with explanation about the simplification achieved by changing the order.

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Chapter 16.2, Problem 34E

Chapter 16.2, Problem 36E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The value of the integral ∫ 0 1 ∫ y = x 1 x e y 3 d y d x in reversed order of integration with explanation about the simplification achieved by changing the order.

Solution Summary: The author explains the value of the integral 0 1 x e y 3 in reversed order of integration with explanation about the simplification achieved by changing the order.

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The value of the integral $\int_{0}^{1} \int_{y = x}^{1} x e^{y^{3}} d y d x$ in reversed order of integration with explanation about the simplification achieved by changing the order.

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Chapter 16 Solutions

The value of the integral ∫ 0 1 ∫ y = x 1 x e y 3 d y d x in reversed order of integration with explanation about the simplification achieved by changing the order.

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The value of the integral $\int_{0}^{1} \int_{y = x}^{1} x e^{y^{3}} d y d x$ in reversed order of integration with explanation about the simplification achieved by changing the order.