Explanation Given information: The figure of the domain D is given as, Formula used: In an iterated integral where d y precedes d x , integration is performed first with respect to y ∫ c d ( ∫ a b f ( x , y ) d y ) d x where c ≤ x ≤ d and a ≤ y ≤ b Calculation: This domain contains the area between two lines with the equations of y = x and y = x 2 . We define the limit of x according to these formulas. Upper limit ⇒ y = x x = y Lower limit ⇒ y = x 2 x = 2 y Also, it is clear that the limit of y as 1 ≤ y ≤ 2 . The integral should be written for these limits of the domain. ∬ D sin y y d A = ∫ 1 2 ( ∫ y 2 y ( sin y y ) d x ) d y = ∫ 1 2 ( sin y y ∫ y 2 y ( 1 ) d x ) d y = &#

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 16.2, Problem 43E

To determine

The integral of $∬Dsinyy dA$ for the domain in the given figure.

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Chapter 16.2, Problem 42E

Chapter 16.2, Problem 44E

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Chapter 16 Solutions

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The integral of ∬ D sin y y d A for the domain in the given figure.

Solution Summary: The author explains how the integral of displaystyle is written for the domain in the given figure.

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The integral of $∬Dsinyy dA$ for the domain in the given figure.

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Chapter 16 Solutions