Consider f and c below. f(x, y) = 6xy2 i + 6x2y j c: r(t) = t + sin 1 2 πt , t + cos 1 2 πt , 0 ≤ t ≤ 1 (a) find a function f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c ∇f · dr along the given curve c.

a. If is a gradient field of a scalar function , then

From these equations we can find

b. By the gradient theorem (i.e. fundamental theorem of calculus for line integrals),

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.