consider the vector field F(x,y,z)=< 2xyz, x²z, x²y +1 >.

a) show that F is irrational (curl F equivalent to 0)

b) quote a theorem to conclude that F is conservative.

c) compute a potential function of F

d) compute the line integral of F along the curve C parametrized by r(t)= (t², t⁴, t⁶ ), for 0

e) Let now F(x,y,z)= < 2xyz, x²z, x²y + 2zcos(z²+1) >. Compute the line integral of F

along the curve parameterized by r(t)= (t², t⁴, t⁶), for 0