定積分の計算

定理 5.12 (置換積分)  

$$\int_{a}^{b}f(x)\,dx= \int_{\phi^{-1}(a)}^{\phi^{-1}(b)}f(\phi(t))\phi'(t)\,dt= \int_{\phi^{-1}(a)}^{\phi^{-1}(b)}f(\phi(t))\frac{dx}{dt}dt$$ (718)

定理 5.13 (部分積分)  

$$\int_{a}^{b}f'(x)g(x)\,dx= [f(x)g(x)]_{a}^{b}- \int_{a}^{b}f(x)g'(x)\,dx$$ (719)

Kondo Koichi
Created at 2002/09/12