Explanation Given: ∫ 0 1 / 2 ∫ 3 x 1 − x 2 x d y d x Calculation: The domain is given as D : 0 ≤ x ≤ 1 2 , 3 x ≤ y ≤ 1 − x 2 y = 3 x ⇒ r sin θ = 3 r cos θ So tan θ = 3 , θ = π 3 Therefore D : 0 ≤ r ≤ 1 , π 3 ≤ θ ≤ π 2 f ( x , y ) = x = r cos θ and d y d x = r d r d θ ⇨ ∫ 0 1 / 2 ∫ 3 x 1 − x 2 x d y d x = ∫ π / 3 π / 2

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 9E

To determine

A sketch of the region of integration $\int_{0}^{1 / 2} \int_{\sqrt{3} x}^{\sqrt{1 - x^{2}}} x d y d x$ and evaluate by changing to polar coordinates.

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Chapter 16.4, Problem 8E

Chapter 16.4, Problem 10E

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Chapter 16 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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A sketch of the region of integration ∫ 0 1 / 2 ∫ 3 x 1 − x 2 x 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 $\int_{0}^{1 / 2} \int_{\sqrt{3} x}^{\sqrt{1 - x^{2}}} x d y d x$ and evaluate by changing to polar coordinates.

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Chapter 16 Solutions

A sketch of the region of integration ∫ 0 1 / 2 ∫ 3 x 1 − x 2 x 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 ∫01/2∫3x1−x2x dy dx and evaluate by changing to polar coordinates.

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Chapter 16 Solutions

A sketch of the region of integration $\int_{0}^{1 / 2} \int_{\sqrt{3} x}^{\sqrt{1 - x^{2}}} x d y d x$ and evaluate by changing to polar coordinates.