A table of values of a function with continuous gradient is given

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Accumulation in Applied Contexts

Problem

A table of values of a function

f

with continuous gradient is given. Find

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

, where

C

has parametric equations

x = t^2 + 1 \quad y = t^3 + t \quad 0 \le t \le 1

x \ y	0	1	2
0	1	6	4
1	3	5	7
2	8	2	9