\[ \begin{aligned} \int_{0}^{\pi} x^{2} \cos x d x &=-\left.\dfrac{d^{2} I(a)}{d a^{2}}\right|_{a=1} \\ &=-\left.\left.\dfrac{d^{2}}{d a^{2}}\left(\dfrac{\sin a \pi}{a}\right)\right|_{a=1}\right|_{a=1...∫π0x2cosxdx=−d2I(a)da2|a=1=−d2da2(sinaπa)|a=1|a=1=−dda(aπcosaπ−sinaπa2)|a3)|a=1=−(a2π2sinaπ+2aπcosaπ−2sinaπ−2π.
\[ \begin{aligned} \int_{0}^{\pi} x^{2} \cos x d x &=-\left.\dfrac{d^{2} I(a)}{d a^{2}}\right|_{a=1} \\ &=-\left.\left.\dfrac{d^{2}}{d a^{2}}\left(\dfrac{\sin a \pi}{a}\right)\right|_{a=1}\right|_{a=1...\boldsymbol{\begin{aligned} \int_{0}^{\pi} x^{2} \cos x d x &=-\left.\dfrac{d^{2} I(a)}{d a^{2}}\right|_{a=1} \\ &=-\left.\left.\dfrac{d^{2}}{d a^{2}}\left(\dfrac{\sin a \pi}{a}\right)\right|_{a=1}\right|_{a=1} \\ &\left.=-\left.\dfrac{d}{d a}\left(\dfrac{a \pi \cos a \pi-\sin a \pi}{a^{2}}\right)\right|_{a^{3}}\right)\left.\right|_{a=1} \\ &=-\left(\dfrac{a^{2} \pi^{2} \sin a \pi+2 a \pi \cos a \pi-2 \sin a \pi}{-2 \pi .}\right. \end{aligned} \label{A.75}}
