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2) Evaluate the following double integrals: a) (x cosy) dA where D is bounded by y = 0, y = 12, and a = 1
2) Evaluate the following double integrals: a) (x cosy) dA where D is bounded by y = 0, y = 12, and a = 1 b) (2x - y) dA where D is bounded by the circle centered at the origin with radius 2 3) Evaluate 4) Evaluate the following triple integrals: a ) (xy) dV where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), (0,0,3) b) JJJ. x2e'dV where E is bounded by the parabolic cylinder z = 1 - y' and the planes z = 0, x = 1, and r = -1 5) a) Use polar coordinates to evaluate cos(22 + y?) dA where R is the region that lies above the x-axis within the circle x2 + y2 = 9 b) Use cylindrical coordinates to evaluate (x2 + y2)3/2dz dy dx 9-12-y2 c) Use spherical coordinates to evaluate zvx2 + y2 + z2dz dy dx2) a) (1 - cos 1) b) 0 3 3-1) 4) a ) 8 b) 3e TT 5) a) sin 9 8TT b) 35 243TT c) 5
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