MATH 222 Midterm: MATH 222 KSU Test 3f98
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To receive credit you must show your work. (15) 1. A mass distribution occupies the region in the rst octant which is enclosed by the surfaces y = x2 , y = x , z = 1 , z = 2 + x . If the mass density function is (x, y, z) = 10y units of mass/unit volume, calculate the total mass in the region. A mass distribution occupies the region which is above the surface z = px2 + y2 and under the plane z = 2 . If the mass density function is (x, y, z) = z2 , use a triple integral in spherical coordinates to calculate the total mass. Calculate the area of that part of the paraboloid z = x2 + y2 which is between the planes z = 1 and z = 9 . The force eld ~f = y~i x~j acts on an object as it moves in the plane.