\[ \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...\[ \begin{aligned} \int_{0}^{\pi} x^{2} \cos x d x &=-\left.\dfrac{d^{2} I(a)}{d a^{2}}\right|_{a=1} \\ &=-\left.\left.\dfrac{d^{2}}{d a^{2}}\left(\dfrac{\sin a \pi}{a}\right)\right|_{a=1}\right|_{a=1} \\ &\left.=-\left.\dfrac{d}{d a}\left(\dfrac{a \pi \cos a \pi-\sin a \pi}{a^{2}}\right)\right|_{a^{3}}\right)\left.\right|_{a=1} \\ &=-\left(\dfrac{a^{2} \pi^{2} \sin a \pi+2 a \pi \cos a \pi-2 \sin a \pi}{-2 \pi .}\right. \end{aligned} \label{A.75} \]
Integration is typically a bit harder. Imagine being given the last result in Equation 8.4.2 and having to figure out what was differentiated in order to get the given function.
