$$a_0 =\dfrac 1{2\pi}\int\limits_0^{2\pi} f(2) dx =\dfrac 1{2\pi} \int\limits_0^{2\pi} \dfrac {(3x^2-6\pi x + 2\pi^2)}{12} dx = \dfrac 1{24\pi}[x^3-3\pi x^2 + 2\pi x^2 ]_0^{2\pi}$$

$=\dfrac 1{24\pi} [8\pi^3-12\pi^3+4\pi^3]=0 \\ an =\dfrac 1{\pi} \int\limits_0^{2\pi}f(x) \cos(nx) dx =\dfrac 1\pi \int\limits_0^{2\pi}\dfrac {(3x^2-\pi x +2\pi^2)}{12}\cos nx \space dx \\ \dfrac 1{12\pi}[ (3x^2-6\pi x +2\pi^2 ) \dfrac {8mnx}n …