그래프와 치환 정적분

$2 x + 1 = t$로 놓으면 $x = 0$일 때 $t = 1$, $x = 1$일 때 $t = 3$ $2 dx = dt$, $\displaystyle dx = \frac{1}{2} dt$ $\displaystyle \int _{0} ^{1} f ( 2 x + 1 ) dx$$\displaystyle = \int _{1} ^{3} f ( t ) . \frac{1}{2} dt$$\displaystyle = \frac{1}{2} \int _{1} ^{3} f ( t ) dt$ $\displaystyle = \frac{1}{2} \left( \int _{1} ^{2} f ( t ) dt + \int _{2} ^{3} f ( t ) dt \right)$$\displaystyle = \frac{1}{2} \left( \int _{1} ^{2} ( 2 t - 1 ) dt + \int _{2} ^{3} 3 dt \right)$ $\displaystyle = \frac{1}{2} \left( \left[ t ^{2} - t \right] _{1} ^{2} + [ 3 t ] _{2} ^{3} \right)$$\displaystyle = \frac{1}{2} ( 2 + 3 )$$\displaystyle = \frac{5}{2}$