Integrate the vector field F=(:x,1:) along the line segment from (-1,1) to (1,-3) in two ways:(a) First, use a parametrization to explicitly calculate the line integral,(b) Then verify F is conservative, find a potential, and use the fundamental theorem of line integrals.Let F=(:excosy,-lonxsiny:). Compute CF*Tds, where C is the piecewise linear curve that starts at (0,), goes up to (1,5), over to (3,8), down to (5,6), and then doubles back to (1,2).Let F(x,y,z)=(yz)i(xz)j(xy)k.(a) Is F conservative? If so, find a potential for F.(b) Evaluate CF*dr, where C consists of line segments from (0,0,0) to (1,0,1) and from (1,0,1) to (0,1,2).Consider the vector field F=(:y-x,x:).(a) Determine whether or not F is conservative; if it is, find a potential.(b) Calculate the circulation oCF*Tds and flux oCF*nds around the circle C given by x2y2=4, oriented counterclockwise. Please answe all four questions and do not use chatgpt