Evaluate , where and is the curve…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Evaluate

\int_C \nabla f \cdot d\mathbf{r}

, where

f(x, y, z) = xy^2z + x^2

and

C

is the curve

x = t^2, y = e^{t-1}, z = t^2 + t, -1 \le t \le 1