4. Using cylindrical coordinates, evaluate IIIe'l'EMJ' 2a! V where Q is the solid Q bounded by the cylinder x2 + y2 = 1, the xy plane and the plane 2 = 2. (10 points) 5. Consider [ F . dr where F(x, y) = (ety2 + li+ (2yet + 3y2 )j and C is the semicircular path from (0, 0) to (0,2) as shown in the figure. a) Find a scalar function f so that Vf = F where the vector field F is defined F = (exy2 + 1, 2ye* + 3y2). (7 points) 2- 1- X b) Using the information from part a), or otherwise find | F . dr . (3 points)6. Evaluate the following integral by changing the order of integration or otherwise: I: I: sin(y2)dydx (7 points) 7. Determine whether the vector field (xye* + 2x, 2y + ex ) is conservative. Show the work that justifies your answer. (3 points)