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)9. a) Show that the line integral (2x y )dx +(2xy2 )dy is NOT independent of path. C (5 points) b) Using Green's theorem, find find f (2xy + x3) dx + (2x2 + 2y3) dy where C consists of the 4 line segments (0, 0) -> (1, 0) ->(1,1) -> (0,1) -> (0,0). (5 points)