1. Evaluate the line integral (x2 + y2 + z? ) ds where C is the curve given by r(t) = sin 2ti - cos 2t j - k, 0 E t = 1. 2. Determine the mass and centre of mass of a thin wire in the shape of the first quadrant part of a circle centre the origin radius a if the density function is p(x, y) = kxy. 3. Compute the value of F . dr C if F = -yi + xj and C is a semicircle from (-1, 1) to (1, -1). 4. Let f = ey - xy, F = Vf and C a curve parametrization, 1 s t s 2. Compute the line integral of F over C.5. Consider a new curve C parametrizationtesint, sint - cost), 0 = t = 1 but with F still as in the previous problem. Determine F . dr 6. Check whether or not F = cos xi+ (y sin x + sin z)j - x cosz k is a conservative vector field. 7. Let F = (1+ xe >)i - e-j. Show that F is conservative and, hence, use the Fundamental Theorem for Line Integrals to determine the work done by the force F in moving an object from (0, 1) to (2, 0)