272t3as08sol

272t3as08sol - Mat 272 Test 3 Dr Firoz 1 A 1 Evaluate the...

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Unformatted text preview: Mat 272 Test 3 Dr. Firoz 1 A 1. Evaluate the double integral , [0,1] [0,4] x x R e y e dxdy R + = × ∫∫ . Show complete work. Sol: 1 4 0 0 13.3 x x x x R e y e dxdy e y e dxdy + = + = ∫∫ ∫ ∫ 2. Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. ( , ) ( , ) R f x y dA f x y dydx---- = ∫∫ ∫ ∫ y x = R 2 y x = Solution: 2 1 ( , ) ( , ) x R x f x y dA f x y dydx = ∫∫ ∫ ∫ 3. Write down the double integral and also triple integral to find the volume of the tetrahedron bounded by the coordinate planes and the plane 4 4 2 z x y = -- . Do not evaluate the integrals. Solution: 1 2 2 x D zdA z dydx z dydx----- = = ∫∫ ∫ ∫ ∫ ∫ 4 4 2 1 2 2 x y x V dv dzdydx--- = ∫∫ ∫ ∫ ∫ ∫ Mat 272 Test 3 Dr. Firoz 2 4. Use spherical coordinate to evaluate 2 2 ( ) H x y dv + ∫∫∫ , where H is the hemispherical region that lies above the xy-plane and below the sphere 2 2 2 1 x y z + + = ....
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This note was uploaded on 05/09/2008 for the course MAT 272 taught by Professor Firoz during the Spring '08 term at ASU.

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272t3as08sol - Mat 272 Test 3 Dr Firoz 1 A 1 Evaluate the...

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