7.2 definite integral — ગણિત ધોરણ 12 સાયન્સ — Question

$\text { Put } 2 x+1=t, d x=\frac{d t}{2}$

$I=\frac{1}{2} \int_{-1}^{1} \frac{t^{2}+2}{1+e^{t}}$

$2 \mathrm{I}=\frac{1}{2} \int_{-1}^{1}\left(\mathrm{t}^{2}+2\right) \mathrm{dt}$

$2 \mathrm{I}=\frac{1}{2} \times 2 \int_{0}^{1}\left(\mathrm{t}^{2}+2\right) \mathrm{dt}$

$2 \mathrm{I}=\left(\frac{t^{3}}{3}+2 t\right)_{0}^{1}$

$I=\frac{7}{6}$