Explanation Given: ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 Calculation: Consider the given integral ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 The given region is D : 0 ≤ y ≤ 1 , − 1 − y 2 ≤ x ≤ 1 − y 2 This is the upper half of the unit circle with center at origin and so it can also be defined as D : − 1 ≤ x ≤ 1 , 0 ≤ y ≤ 1 − x 2 Therefore, ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 = ∫ − 1 1 ∫ 0 1 − x 2 y d x d y ( 1 + x 2 + y 2 ) 2 Thus, the integral ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 can be rewritten as ∫ − 1 1 ∫ 0 1 − x 2 y d x d y ( 1 + x 2 + y 2 ) 2 by changing the order of integration...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16, Problem 22CRE

To determine

To calculate:

Rewrite $\int_{0}^{1} \int_{- \sqrt{1 - y^{2}}}^{\sqrt{1 - y^{2}}} \frac{y d x d y}{{(1 + x^{2} + y^{2})}^{2}}$ by interchanging the order of integration and evaluate.

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Chapter 16, Problem 21CRE

Chapter 16, Problem 23CRE

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Rewrite ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 by interchanging the order of integration and evaluate.

Solution Summary: The author explains how the integral can be rewritten by interchanging the order of integration and evaluate.

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To calculate:

Rewrite $\int_{0}^{1} \int_{- \sqrt{1 - y^{2}}}^{\sqrt{1 - y^{2}}} \frac{y d x d y}{{(1 + x^{2} + y^{2})}^{2}}$ by interchanging the order of integration and evaluate.

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Chapter 16 Solutions

Rewrite ∫ 0 1 ∫ − 1 − y 2 1 − y 2 y d x d y ( 1 + x 2 + y 2 ) 2 by interchanging the order of integration and evaluate.

Solution Summary: The author explains how the integral can be rewritten by interchanging the order of integration and evaluate.

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To calculate: Rewrite ∫01∫−1−y21−y2ydxdy(1+x2+y2)2by interchanging the order of integration and evaluate.

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Chapter 16 Solutions

To calculate:

Rewrite $\int_{0}^{1} \int_{- \sqrt{1 - y^{2}}}^{\sqrt{1 - y^{2}}} \frac{y d x d y}{{(1 + x^{2} + y^{2})}^{2}}$ by interchanging the order of integration and evaluate.