Chapter 17.3, Problem 42E

Using the Fundamental Theorem for line integrals verify that the Fundamental Theorem for line integrals can be used to evaluate the given integral, and then evaluate the integral.

42. ${\displaystyle \underset{C}{\int }\nabla \left(1+x^{2}yz\right)\cdot dr\text{,}}$ where C is the helix r(t) = $\langle \cos 2t,\sin 2t,t\rangle$, for 0 ≤ t ≤ 4π