Chapter 17, Problem 25RE

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

25.     $F=\nabla \left(xyz\right);C\text{:}r\left(t\right)=\langle \cos t,\sin t,t/\pi \rangle ,$ for 0 ≤ t ≤ π