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Unformatted text preview: 5. (10 points) Evaluate R 1 R 1 √ y √ x 3 + 1 dxdy by interchanging the order of integration. R 1 R 1 √ y √ x 3 + 1 dxdy = R R dy dx = 4 6. (10 points) Find the mass of the solid inside the sphere x 2 + y 2 + z 2 = 9 and above the cone z = p x 2 + y 2 , if the density is δ ( x,y,z ) = z 2 . mass = 7. (15 points) Apply Green’s Theorem to evaluate H C ( x 2 cos x + 2 y ) dx +( y 3 + 5 x ) dy where C is the triangle with vertices (0 , 0), (1 , 0) and (0 , 2), traversed in the counterclockwise direction. H C ( x 2 cos x + 2 y ) dx +( y 3 + 5 x ) dy = 5 8. (15 points) Let S be the cylindrical region x 2 + y 2 ≤ 4, 0 ≤ z ≤ 3, and let n be the outward unit normal to the boundary ∂S of S . If F ( x,y,z ) = ( x 3 z + y 2 ) i + ( x 2 + y 3 z ) j + ( x 2 + y ) k , ﬁnd the ﬂux of F across ∂S . ﬂux = 6...
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 Spring '08
 Gregorac
 Math, Calculus, Parametric equation

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