Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f such that f = ∇f. f(x, y) = x3 3+ y3 3 correct: your answer is correct. (b) use part (a) to evaluate c ∇f · dr along the given curve c.

In this exercise we have to perform the parameterization of the given function and we will have:

In there is some scalar function such that:

Then we want to find such that:

So the vector filed is conservative, which means the fundamental theorem applies; the line integral of along any path parameterized by some vector-valued function over is given by:

In the case:

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