Explanation Approach: According to Fubini’s theorem ∫ a b ∫ c d f ( x , y ) d y d x = ∫ c d ∫ a b f ( x , y ) d x d y Calculation: Consider the integral. ∬ R 2 x + y d x d y Apply boundary conditions, the integral becomes, ∫ 2 5 ∫ 1 3 2 x + y d x d y Integrate with respect to x while treating y as constant. Let, u = 2 x + y d u = 2 x The integral will be ∫ 2 x + y d x = ∫ u 2 d u = ∫ u 1 2 2 d u Thus, the integral, ∫ 1 3 2 x + y d x = ∫ y + 2 y + 6 u 1 2 2 d u = 2 3 [ u 3 2 2 ] y + 2 y + 6 = 1 3 [ ( 6 + y ) 3 2 − ( 2 + y ) 3 2 ] Integrate with respect to y while treating x as constant

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ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

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Chapter 9.CR, Problem 70CR

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To find:

The value of the integral ∬R2x+ydxdy over the boundaries 1≤x≤3, 2≤y≤5.

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Chapter 9.CR, Problem 69CR

Chapter 9.CR, Problem 71CR

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Chapter 9 Solutions

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The value of the integral ∬ R 2 x + y d x d y over the boundaries 1 ≤ x ≤ 3 , 2 ≤ y ≤ 5 .

Solution Summary: The author explains Fubini's theorem, wherein the value of the integral is sqrt2x+ydxdy.

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To find:

The value of the integral ∬R2x+ydxdy over the boundaries 1≤x≤3, 2≤y≤5.

Want to see the full answer?

Chapter 9 Solutions

The value of the integral ∬ R 2 x + y d x d y over the boundaries 1 ≤ x ≤ 3 , 2 ≤ y ≤ 5 .

Solution Summary: The author explains Fubini's theorem, wherein the value of the integral is sqrt2x+ydxdy.

Concept explainers

Videos

To find: The value of the integral ∬R2x+ydxdy over the boundaries 1≤x≤3, 2≤y≤5.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of the integral ∬R2x+ydxdy over the boundaries 1≤x≤3, 2≤y≤5.