brief
設函式\(f(x)\)在區間\([a,b]\)上連續變化，函式\(x= \varphi (t)\)在區間\([\alpha,\beta]\)上具有連續的導數
當\(t\)在區間\([\alpha,\beta]\)上變化時，\(x= \varphi (t)\)的值在\([a,b]\)上變化
又 \(\varphi(\alpha)=a, \quad \varphi(\beta)=b\)
則:
\[\int_{a}^{b} f(x)dx=\int_{\alpha}^{\beta} f[\varphi(t)]\varphi '(t)dt
\]