Explanation Given: The function is, f ( x , y ) = y ( 2 x + 5 y 2 ) . The rectangular region, R = { ( x , y ) | 0 ≤ x ≤ 2 , 1 ≤ y ≤ 3 } . Calculation: The value of ∬ R 3 ( 2 x + 5 y 2 ) d x d y is computed as follows. Integrate first with respect to x. ∬ R y ( 2 x + 5 y 2 ) d x d y = ∫ 1 3 [ ∫ 0 2 y ( 2 x + 5 y 2 ) d x ] d y = ∫ 1 3 [ ∫ 0 2 y ( 2 x + 5 y 2 ) − 1 2 d x ] d y = ∫ 1 3 [ y ⋅ 1 2 ⋅ ( 2 x + 5 y 2 ) 1 2 1 2 ] 0 2 d y = ∫ 1 3 [ y ⋅ 1 2 ⋅ 2 ( 2 x + 5 y 2 ) 1 2 ] 0 2 d y ∫ 1 3 [ y ( 2 x + 5 y 2 ) 1 2 ] 0 2 d y Apply the limit of x. ∬ R y ( 2 x + 5 y ) 2 d x d y = ∫ 1 3 [ y ( 2 ( 2 ) + 5 y 2 ) 1 2 − y ( 2 ( 0 ) + 5 y 2 ) 1 2 ] d y = ∫ 1 3 [ y ( 4 + 5 y 2 ) 1 2 − y ( 5 y 2 ) 1 2 ] d y Integrate with respect to y

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 17.6, Problem 26E

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To find: The value of ∬Ry(2x+5y2)dxdy over the rectangular region R.

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Chapter 17.6, Problem 25E

Chapter 17.6, Problem 27E

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Chapter 17 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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The value of ∬ R y ( 2 x + 5 y 2 ) d x d y over the rectangular region R.

Solution Summary: The author explains how the value of displaystyle 'underset' is computed over the rectangular region R.

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To find: The value of ∬Ry(2x+5y2)dxdy over the rectangular region R.

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Chapter 17 Solutions