Explanation Given : ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y Calculation : Step 1: The limits of integration correspond to the inequalities describing the following shaded horizontally simple region: 0 ≤ y ≤ 4 , y ≤ x ≤ 2 Step 2: The region can also be expressed as a vertically simple region. Rewriting the equation x = y in the form y = x 2 , we define D by the following inequalities: 0 ≤ x ≤ 2 , 0 ≤ y ≤ x 2 Step 3: The corresponding iterated integral is ∫ 0 2 ∫ 0 x 2 4 x 2 + 5 y d y d x When we evaluate this integral ∫ 0 2 ∫ 0 x 2 4 x 2 + 5 y d y d x = ∫ 0 2 ( ∫ 0 x 2 ( 4 x 2 + 5 y ) 1 / 2 d y ) d x

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.2, Problem 29E

To determine

The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.

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Chapter 16.2, Problem 28E

Chapter 16.2, Problem 30E

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Chapter 16 Solutions

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The sketch of the domain of integration of ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y and to evaluate the integration which is changed as an iterated integral in the opposite order.

Solution Summary: The author explains the sketch of the domain of integration of 0 4 y, which is sketched such that the limits correspond to the inequalities describing the following shaded horizontally simple region.

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The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.

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Chapter 16 Solutions

The sketch of the domain of integration of ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y and to evaluate the integration which is changed as an iterated integral in the opposite order.

Solution Summary: The author explains the sketch of the domain of integration of 0 4 y, which is sketched such that the limits correspond to the inequalities describing the following shaded horizontally simple region.

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The sketch of the domain of integration of ∫04∫y24x2+5ydxdy and to evaluate the integration which is changed as an iterated integral in the opposite order.

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Chapter 16 Solutions

The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.