Consider F and C below.
F(x, y, z) = e<sup>y</sup>i + xe<sup>y</sup>j + (z+1)e<sup>z</sup>k
C: r(t) = 9t i + t<sup>2</sup>j + t<sup>3</sup>k, 0 ? t ? 1
(a) Find a function f such that F = ?f.
(b) Use part (a) to evaluate \(\int_C \nabla f \cdot d\vec{r}\) along the given curve C.