Explanation Given: ∫ 0 2 ∫ x 3 x y d y d x Calculation: The domain is given as D : 0 ≤ x ≤ 2 , x ≤ y ≤ 3 x D : 0 ≤ r cos θ ≤ 2 , r cos θ ≤ r sin θ ≤ 3 r cos θ ⇨ D : 0 ≤ r ≤ 2 sec θ , π 4 ≤ θ ≤ π 3 ⇨ ∫ 0 2 ∫ x 3 x y d y d x = ∫ π / 4 π / 3 ∫ 0 2 sec θ r sin θ r d r d θ = ∫ π / 4 π / 3 ∫ 0 2 sec θ r 2 sin θ d r d θ = ∫ π / 4 π / 3 sin θ d θ r 3 3 | 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.4, Problem 12E

To determine

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

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Chapter 16.4, Problem 11E

Chapter 16.4, Problem 13E

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Chapter 16 Solutions

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

Solution Summary: The author evaluates the region of integration by changing to polar coordinates.

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

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Chapter 16 Solutions

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

Solution Summary: The author evaluates the region of integration by changing to polar coordinates.

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A sketch of the region of integration ∫02∫x3xy dy dx and evaluate by changing to polar coordinates.

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Chapter 16 Solutions

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