1. If F = grad(x2 + y'), find J F . di where C is the quarter of the circle x2 + y = 4 in the first quadrant, oriented counterclockwise. 2. Find f if grad f = 2ryi+ 12j. 3. Find f if grad f = 2xyi+ (x2 + 8y3) j. 4. Let f(x, y, 2) = x2 + 243 + 324 and F = grad f. Find Jo, F . di where C consists of four line segments from (4, 0, 0) to (4, 3, 0) to (0, 3, 0) to (0, 3, 5) to (0, 0, 5). 5. Use the Fundamental Theorem for Line Integrals to calculate fo F . dr where F = (x+2) i + (2y + 3) j and C is the line from (1, 0) to (3, 1). 6. Use the Fundamental Theorem for Line Integrals to calculate fo F . dF where F = 24/3 7+ ely; and C is the unit circle oriented clockwise. 7. Use the Fundamental Theorem for Line Integrals to calculate fo F . dr where F = yervi+ xev j+ (cos z) k and C is the curve consisting of a line from (0, 0, 7) to (1, 1, w) followed by the parabola z = wr in the plane y = 1 to the point (3, 1,9TT). 8. Compute (cos(ry)esin(zy) (yitxj) + k) . di where C is the line from (7, 2, 5) to (0.5, 7, 7). 9. Decide whether the vector field G(x,y) = (x2 -y?) i-2ry j could be a gradient vector field. Justify your