\[ \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.
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.
