Chapter 17, Problem 24RE

Evaluating line integrals Evaluate the line integral ${\displaystyle {\int }_{C}F\cdot dr}$ for the following vector fields F and curves C in two ways.

a.    By parameterizing C

b.    By using the Fundamental Theorem for line integrals, if possible

24.     $F=\nabla \left(x^{2}y\right);C\text{:}r\left(t\right)=\langle 9-t^2,t\rangle ,$ for 0 ≤ t ≤ 3