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Let E be the region in the first octant of [R3 that lies inside the paraboloid z = -x2 - y2 + 2 and the

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Let E be the region in the first octant of [R3 that lies inside the paraboloid z = -x2 - y2 + 2 and the cone 2 = \\fo + yz. a) Set up {but do not evaluate) iterated integrals that compute the volume of E 1.- in Cartesian coordinates, with an order of integration dxdydz. 2.- in cylindrical coordinates, with an order of integration dzdrd. 3.- in spherical coordinates, with an order of integration dpdqbd. Be sure to provide some justification for your answers. 1)) Evaluate one of your integrals from part (a). [To check your work, you may want to evaluate them all. But only submit one evaluation. The TAs will only grade one.]

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