Boundary Values & Fourier Series · Easy problem

The half-range cosine series of $f(x) = x$ on $[0, 2]$ is $\dfrac{a_0}{2} + \sum_{n\ge1} a_n\cos\dfrac{n\pi x}{2}$ with $a_n = \dfrac{2}{L}\displaystyle\int_0^L f(x)\cos\dfrac{n\pi x}{L}\,dx$ and $L = 2$, i.e. $a_n = \displaystyle\int_0^2 f(x)\cos\dfrac{n\pi x}{2}\,dx$. Find the constant term $\dfrac{a_0}{2}$.