Consider f and c below. f(x, y, z) = yzexzi + exzj + xyexzk,

c. r(t) = (t2 + 5)i + (t2 − 3)j + (t2 − 5t)k, 0 ≤ t ≤ 5 (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c f · dr along the given curve

c.

We're looking for a scalar function such that . This means

In the second PDE, integrate both side with respect to :

Differentiate both sides of this with respect to :

Differentiate this with respect to :

for some constant , so that

By the fundamental theorem of calculus, this line integral has a value of

since

hey! so 1 (25) out of 4 (100) is 25 so your answer is 25%. it's like quarters!