(915, #13)

(a) Find a potential f for F(x, y) = < 2 x y³, 3 x² y²>..

(b) Use (a) to evaluate

along the curve r(t) = < sin(t), 1 + t²>.

Solution: (a) Since F is conservative we can use the usual method for finding a potential:

b) The endpoints of r(t) = < sin(t), 1 + t²>, t = 0..Pi/2 are r(0) = <0,1> and r(Pi/2) = <1, 1 +(Pi/2)². Thus

by C.A.H.