Please solve all.

1) Consider the conservative vector field F(x.y) = (vex + sin(y))i + (ex + xcos(y))j a. Determine if F is conservative b. If conservative, find the potential function ff 2) Consider the vector field F(Xy) = 2xyi + (x2 - y)j on an object over P(0,0) and Q(2,1) a. Use a parameterization to find the work done from P to Q b. Verify that F is conservative c. Find the potential function (x, v) d. Use the fundamental theorem of line integrals to find the work done on the object e. Compare the answers from parts a and d. Comment. 3) Consider the line integral fox dy + ydx where C is the boundary of the triangular region with vertices P(0,0), Q(1,1), and R(0,1). Compute the line integral in two ways: a. Using 3 parameterizations (i.e. segments PQ, QR, and RP). b. Using Greene's Theorem. Be sure to show that the boundary satisfies the conditions to use Greene's Theorem. 4) Evaluate f (4x3 + siny?)dy -(4y3 + cosx2 ) dx where C is bound by a circle of radius 4 oriented in a counterclockwise orientation