15.3-15.4soln

15.3-15.4soln - Z √ π Z √ π y cos ( x 2 ) dxdy (b) Z...

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MATH 231 Group Work Quiz Related 1. Evaluate the double integral: (a) ZZ D (2 x + y ) dA where D is the region bounded by y = x and y = x 2 (b) Z 1 0 Z 2 - y 2 y ( x + y ) dxdy (c) ZZ D 2 x 2 y dA where D is the triangular region with vertices (0 , 0), (1 , 2), and (0 , 3) (d) ZZ D ( x +4 y ) dA where D is the region bounded by the circle with center the origin and radius 4 (e) Z 2 0 Z 2 x - x 2 0 p x 2 + y 2 dy dx Answers: (a) 9 20 (b) 2 2 3 (c) 9 10 (d) 0 (e) 16 9 2. Sketch the region of integration and evaluate the integral. (a)
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Unformatted text preview: Z √ π Z √ π y cos ( x 2 ) dxdy (b) Z 1 Z 1 x e x/y dy dx Answers: (a) 0 1-5-4-3-2-1 1 2 3 4 5-2-1 1 2 (b) 1 2 ( e-1)-2.4-2-1.6-1.2-0.8-0.4 0.4 0.8 1.2 1.6 2 2.4-1.2-0.8-0.4 0.4 0.8 1.2 3. Find the average value of x sin y over the region D enclosed by the curves y = 0, y = x 2 , and x = 1. Answer: 3 2 (1-sin 1) 2...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.

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15.3-15.4soln - Z √ π Z √ π y cos ( x 2 ) dxdy (b) Z...

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