Explanation Approach: Double integral over a variable region R can be defined as, if a ≤ x ≤ b , g ( x ) ≤ y ≤ h ( x ) ∬ R f ( x , y ) d y d x = ∫ a b [ ∫ g ( x ) h ( x ) f ( x , y ) d y ] d x Double integral over variable region R can be defined as, if g ( y ) ≤ x ≤ h ( y ) , c ≤ y ≤ d ∬ R f ( x , y ) d y d x = ∫ c d [ ∫ g ( y ) h ( y ) f ( x , y ) d x ] d y Calculation: Given: integral ∬ R ( 2 x + 6 y ) d y d x and boundary 2 ≤ x ≤ 4 , 2 ≤ y ≤ 3 x Integral over a rectangular region can be written as ∬ R ( 4 − 4 x 2 ) d y d x = ∫ 0 1 [ ∫ 0 2 − 2 x ( 4 − 4 x 2 ) d y ] d x Integrate inner integral with respect to y and outer integral with respect to x

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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 9.5, Problem 51E

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To find:

The value of double integral ∬R(4−4x2)dydx in a region R with boundaries 0≤x≤1,0≤y≤2−2x.

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Chapter 9.5, Problem 50E

Chapter 9.5, Problem 52E

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The value of double integral ∬ R ( 4 − 4 x 2 ) d y d x in a region R with boundaries 0 ≤ x ≤ 1 , 0 ≤ y ≤ 2 − 2 x .

Solution Summary: The author explains how the value of double integral displaystyleundersetRiint is defined over a variable region R with boundaries.

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To find:

The value of double integral ∬R(4−4x2)dydx in a region R with boundaries 0≤x≤1,0≤y≤2−2x.

Want to see the full answer?

Chapter 9 Solutions

The value of double integral ∬ R ( 4 − 4 x 2 ) d y d x in a region R with boundaries 0 ≤ x ≤ 1 , 0 ≤ y ≤ 2 − 2 x .

Solution Summary: The author explains how the value of double integral displaystyleundersetRiint is defined over a variable region R with boundaries.

Videos

To find: The value of double integral ∬R(4−4x2)dydx in a region R with boundaries 0≤x≤1,0≤y≤2−2x.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of double integral ∬R(4−4x2)dydx in a region R with boundaries 0≤x≤1,0≤y≤2−2x.