Explanation Given: ∫ ∫ D x 2 + y 2 d A , where D is the region in the first quadrant bounded by the spiral r = θ , the circle r = 1 and the x -axis. Calculation: The given region is bounded by the polar curves spiral r = θ , the circle r = 1 and the x -axis in first quadrant as shown in the graph: It can be seen from the graph that both the polar curves meet at θ = 1 . Thus, in polar coordinates, the region is defined as: D : 0 ≤ θ ≤ 1 , θ ≤ r ≤ 1 Using polar coordinates to evaluate the integral, ∫ ∫ D x 2 + y 2 d A = ∫ 0 1 ∫ θ 1 ( r ) r d r d θ

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 33CRE

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To calculate:

$\int \int_{D} \sqrt{x^{2} + y^{2}} d A$ using polar coordinates.

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Chapter 16, Problem 32CRE

Chapter 16, Problem 34CRE

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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01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY

∫ ∫ D x 2 + y 2 d A using polar coordinates.

Solution Summary: The author explains how to calculate D x 2 + y 2 d A using polar coordinates.

Concept explainers

Videos

To calculate:

$\int \int_{D} \sqrt{x^{2} + y^{2}} d A$ using polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

∫ ∫ D x 2 + y 2 d A using polar coordinates.

Solution Summary: The author explains how to calculate D x 2 + y 2 d A using polar coordinates.

Concept explainers

Videos

To calculate: ∫∫Dx2+y2dAusing polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

To calculate:

$\int \int_{D} \sqrt{x^{2} + y^{2}} d A$ using polar coordinates.