240
(1) 等式\(\displaystyle{\int_{\alpha}^\beta(x-\alpha)(x-\beta)\ dx =-\dfrac{1}{6}(\beta-\alpha)^3}\) を証明せよ。
(2) 次の定積分を求めよ。
(ア) \(\displaystyle{\int_{2}^3(x-2)(x-3)\ dx}\)
(イ) \(\displaystyle{\int_{1-\sqrt{2}}^{1+\sqrt{2}}(x^2-2x-1)\ dx}\)