Explanation Given: ∫ 0 3 ∫ 0 9 − y 2 x 2 + y 2 d x d y Calculation: The domain is given as D : 0 ≤ y ≤ 3 , 0 ≤ x ≤ 9 − y 2 In polar co-ordinates D : 0 ≤ θ ≤ π 2 , 0 ≤ r ≤ 3 , f ( x , y ) = x 2 + y 2 = r and d y d x = r d r d θ ⇨ ∫ 0 3 ∫ 0 9 − y 2 x 2 + y 2

3rd Edition

ISBN: 9781464114885

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 15.4, Problem 8E

To determine

A sketch of the region of integration $\int_{0}^{3} \int_{0}^{\sqrt{9 - y^{2}}} \sqrt{x^{2} + y^{2}} d x d y$ and evaluate by changing to polar coordinates.

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Chapter 15.4, Problem 7E

Chapter 15.4, Problem 9E

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Chapter 15 Solutions

Calculus: Early Transcendentals

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Knowledge Booster

A sketch of the region of integration ∫ 0 3 ∫ 0 9 − y 2 x 2 + y 2 d x d y and evaluate by changing to polar coordinates.

A sketch of the region of integration ∫03∫09−y2x2+y2dx dy and evaluate by changing to polar coordinates.

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Chapter 15 Solutions

A sketch of the region of integration $\int_{0}^{3} \int_{0}^{\sqrt{9 - y^{2}}} \sqrt{x^{2} + y^{2}} d x d y$ and evaluate by changing to polar coordinates.