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quiz_08B - 0 then arctan y/x = θ so ZZ R arctan y/x dA = Z...

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Math 213 — Quiz 8 Name Solution 1. Use polar coordinates to evaluate ZZ R arctan( y/x ) dA . Where R = { ( x, y ) | 1 x 2 + y 2 4 , 0 y x } . In polar coordinates, the region R corresponds to the “rectangle” 1 r 2, 0 θ π/ 4. Moreover, if
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Unformatted text preview: 0 then arctan( y/x ) = θ , so ZZ R arctan( y/x ) dA = Z 2 1 Z π/ 4 θr dθ dr = Z π/ 4 θ dθ ! ±Z 2 1 r dr ² = ± ( π/ 4) 2 2-2 2 ²± 2 2 2-1 2 2 ² = 3 π 2 64...
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