GATE2016-2-26

Question

A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$  on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$.

The curve $C$ is parameterized as follows:$\begin{cases} x=t\\ y=t^2 \text{ and }1\leq t\leq 3 \\ z=3t^2 \end{cases}$.

The value of the integral is ________