I am given the following things: let $M\in \mathbb{R}^{(N\times n)\times(N\times n)}$ be a symmetric matrix. The function $f: \mathbb{R}^{N\times n} \to \mathbb{R}$ is defined as: $$f(\xi):=\langle M\xi, \xi \rangle.$$ I have to show:
$$f\text{ is quasi convex} \Longleftrightarrow \int_{\Omega} f (D\varphi(x)) \,dx \geq 0$$ $\forall \Omega\subseteq \mathbb{R}^n$ open and bounded and for all $\varphi \in C^\infty_0\left(\Omega,\mathbb{R}^N\right)$.
I have absolutly no idea how to start, can someone give me a hint please?