Explanation Given: The integral is ∬ R 2 x 3 e x 2 y d x d y and 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 Approach: Double integral over rectangular region R has specified range for x and y . We can define double integral over rectangular region R as below if a ≤ x ≤ b , c ≤ y ≤ d ∬ R f ( x , y ) d y d x = ∫ a b ∫ c d f ( x , y ) d y d x Or ∬ R f ( x , y ) d x d y = ∫ c d ∫ a b f ( x , y ) d x d y Calculation: Given integral is ∬ R x e x y d x d y and 0 ≤ x ≤ 2 , 0 ≤ y ≤ 1 We can integrate with respect to y first and then with respect to x because from that we don’t need to apply integration by parts and can do integration very easily. We can write integral over rectangular region as ∬ R 2 x 3 e x 2 y d x d y = 2 ∫ 0 1 ∫ 0 1 x 3 e x 2 y d y d x On integrating inner integral with respect to y and outer integral with respect to x

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 9.5, Problem 40E

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To find:

The integral is ∬R2x3ex2ydxdy and 0≤x≤1,0≤y≤1.

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Chapter 9.5, Problem 39E

Chapter 9.5, Problem 41E

Chapter 9 Solutions

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The integral is ∬ R 2 x 3 e x 2 y d x d y and 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 .

Solution Summary: The author explains the value of the integral, which is displaystyleundersetRiint.

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To find:

The integral is ∬R2x3ex2ydxdy and 0≤x≤1,0≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

The integral is ∬ R 2 x 3 e x 2 y d x d y and 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 .

Solution Summary: The author explains the value of the integral, which is displaystyleundersetRiint.

Concept explainers

Videos

To find: The integral is ∬R2x3ex2ydxdy and 0≤x≤1,0≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

To find:

The integral is ∬R2x3ex2ydxdy and 0≤x≤1,0≤y≤1.