1) Show that the vector field F = (3x^2)i + (5z^2)j + (10yz)k is irrotional. Then find a potential function f(x,y,z) such that gradient f = F.
(Ok, so i got the part of showing that F is irrotional. But when i tried figuring out to find the function i got something weird. I am not sure if i got this right. My answer is: f(x,y,z) = x^3 + 5z^2 + 5yz^2 - 5z^2.)
2) Let F(x,y,z) = (8xz)i + (1-6yz^3)j + (4x^2 - 9y^2z^2)k. Show that integral with lower terminal C of (F.dr) is independent of path by finding a potential function f for F.
If you could please help me with these problems much would be appreciated. Thank you