Consider the vector field ⃑(,, ) = ⟨^ − 40,^3 − 40, sec^2(5) − 40 ⟩.

a. Show that F is conservative without determining a potential function.

b. Determine a potential function f for F .

c. Sketch the cone = 2/3 and the sphere p =1 . Parametrize the curve of intersection C of these two surfaces, and use it to set up and evaluate the line integral of F along C.

d. How could you have predicted the result of part c without actually evaluating a line integral?