Answer
$$ f(x,y)=xy+K $$
Work Step by Step
Given $$\nabla f=\langle y,x\rangle$$
Since $$ \nabla f=\left\langle\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right\rangle=\langle y,x\rangle$$
Then
\begin{align*}
\frac{\partial f}{\partial x}&=y\ \ \ \Rightarrow\ \ f=xy+C_1\\
\frac{\partial f}{\partial y}&=x\ \ \ \Rightarrow\ \ f= yx+C_2 \
\end{align*}
Hence
$$ f(x,y)=xy+K $$
