Explanation Given: ∫ ∫ D sin ( x 2 + y 2 ) d A , where D = { π 2 ≤ ( x 2 + y 2 ) ≤ π } Calculation: Consider the region D = { π 2 ≤ ( x 2 + y 2 ) ≤ π } This is the region between the two circles centered at origin and with radii π 2 , π Using polar coordinates, the region can be defined as: D : 0 ≤ θ ≤ 2 π , π 2 ≤ r ≤ π Using polar coordinates to evaluate the integral, ∫ ∫ D sin ( x 2 + y 2 ) d A = Ȣ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16, Problem 34CRE

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To calculate:

$\int \int_{D} \sin (x^{2} + y^{2}) d A$

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Chapter 16, Problem 33CRE

Chapter 16, Problem 35CRE

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∫ ∫ D sin ( x 2 + y 2 ) d A

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

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To calculate: ∫∫Dsin(x2+y2)dA

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Chapter 16 Solutions

To calculate:

$\int \int_{D} \sin (x^{2} + y^{2}) d A$