Question: For the following integrals, choose whether Cartesian coordinates, cylin-drical coordinates, or spherical coordinates would be the best way tofind the integral, and then express the
For the following integrals, choose whether Cartesian coordinates, cylin-drical coordinates, or spherical coordinates would be the best way tofind the integral, and then express the integral as an iterated integralwhere you have determined all of the bounds of integration and ex-pressed the integrand in the new coordinates. You do not need tocompute the integral! (In terms of the definition of best, you canalways avoid chopping the domains that I have given you as long asyou are in the right coordinates and so you should.)(a) :={(x, y, z) in the first octant : x2+ y225, and z 10},z2 dV .(b) :={(x, y, z) in the first octant : x2+ y2+ z225},z2 dV .(c) :={(x, y, z) in the first octant : x + y + z 7},(x2+ y2) dV .(d) :={(x, y, z) : 0 z 4 and x2+ y2+ z225}, z dV .(e) :={(x, y, z) : x2+ y24 and x2+ y2+ z225}, z dV .(f) :={(x, y, z) : x2+ y2 z, x 0, and x2+ y2+ z2144}, x dV .
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