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Unformatted text preview: mass of the object RRR D f dV in: (a) rectangular (Cartesian) coordinates; (b) cylindrical coordinates; (c) spherical coordinates. (d) Now compute one of the integrals you obtained in (a), (b), or (c). (You will only get credit for evaluating one of the three, though you are free to compute more than one as a way to check your answer. Correct evaluation of an integral that is very far from being correct, in case you made a mistake in (a), (b), or (c), will be worth something, but is not necessarily worth full credit on this part.) 2. (30 points) Let R be the region in the plane bounded by the lines y = x , y = x + 2 , y = 3 x , and y = 3 x + 1 . (See Fgure.) Compute RR R 4 x 2 dA . 110.5 0.5 1 1.5321 1 2 3 4 5 6 3. (30 points) Let Σ = { ( x, y, z ) : x 2 + y 2 + z 2 = 1 } be the unit sphere in 3space. Compute the surface integral Z Z Σ x 2 dS. 2...
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 Spring '08
 Wolfe
 Math, Calculus, Coordinate system, Prof. Jonathan Rosenberg

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