1 Problem 6.2.8 Define T(u,v) = (u²-2, 2uv). Let D be the set of (u, v) with u² +² ≤1, 20, v≥0. Find T(D) D. Evaluate ff, dz dy. 2 Problem 6.2.16 Let D be the unit disk. Express + +23/2 dr dy as an integral over [0,1] x [0,2] and evaluate. 3 Problem 6.3.11 Find the mass of the solid ball of radius 5 with density given by 6(x,y,)=2x+2y +2:²+1 assuming the center of the ball is at the origin. 4 Problem 7.1.10 (b) Evaluate the following integral ff(x, y, z) ds, where f(x, y, z) = cos 2 and c:t 5 Problem 7.1.24 (sint, cost, t), te [0,2]. Compute the path integral of f(x,y) = y² over the graph of y = e², x € [0,1]. 6 Problem 7.2.4 (c) Evaluate the following line integral Jeyz dr + zz dy + zy dz, where c consists of straight-line segments joining (1,0,0) to (0,1,0) to (0,0,1).

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