Explanation Approach: Double integral over the rectangular region R has specified range for x and y . Double integral over the rectangular region R can be defined as, for 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, the integral is ∬ R x cos ( x y ) d y d x and the boundaries π 2 ≤ x ≤ π , 0 ≤ y ≤ 1 . Double integral over the rectangular region can be written as, ∬ R x cos ( x y ) d y d x = ∫ π 2 π ∫ 0 1 x cos ( x y ) d y d x On integrating the inner integral with respect to y and the outer integral with respect to x ,

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

Publisher: Pearson Addison Wesley,

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Chapter 9.5, Problem 29E

To determine

To find:

The value of the double integral ∬Rxcos(xy)dydx over the rectangular region R with the boundaries π2≤x≤π, 0≤y≤1.

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Chapter 9.5, Problem 28E

Chapter 9.5, Problem 30E

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The value of the double integral ∬ R x cos ( x y ) d y d x over the rectangular region R with the boundaries π 2 ≤ x ≤ π , 0 ≤ y ≤ 1 .

Solution Summary: The author explains the value of the double integral over the rectangular region R with the boundaries.

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To find:

The value of the double integral ∬Rxcos(xy)dydx over the rectangular region R with the boundaries π2≤x≤π, 0≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

The value of the double integral ∬ R x cos ( x y ) d y d x over the rectangular region R with the boundaries π 2 ≤ x ≤ π , 0 ≤ y ≤ 1 .

Solution Summary: The author explains the value of the double integral over the rectangular region R with the boundaries.

Concept explainers

Videos

To find: The value of the double integral ∬Rxcos(xy)dydx over the rectangular region R with the boundaries π2≤x≤π, 0≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of the double integral ∬Rxcos(xy)dydx over the rectangular region R with the boundaries π2≤x≤π, 0≤y≤1.