I am working the following question:
Question as given:
Evaluate the line integral $\int_{C}cos(z)dx + e^{x}dy + e^{y}dz$, where $C$ is the curve parameterized as $C(t)=(1,t,e^{t}), 0 \leq t \leq 2$.
I have got the following result but I'm not sure if this is correct or if I have made a mistake somewhere?
$\begin{aligned} \int_0^2 cos(e^t)\cdot 0 + e^{1} + e^t \cdot e^t dt &= \int_0^2 e + e^{2t} dt \\ &= \int_0^2 e dt + \int_0^2 e^{2t} dt \\ &= \left[te\right]_0^2 + \left[\frac{e^{2t}}{2}\right]_0^2\\ &= 2e + \frac{e^4}{2}-\frac{1}{2}\\ &= 32.2356. \end{aligned}$