The area of the region bounded by the curve $\mathrm{y}=x^{2}+1$, the lines $\mathrm{x}=1, \mathrm{x}=2$ and…
The area of the region bounded by the curve $\mathrm{y}=x^{2}+1$, the lines $\mathrm{x}=1, \mathrm{x}=2$ and the $\mathrm{X}$ - axis is
$\frac{13}{3}$ sq. units
$\frac{10}{3}$ sq. units
$\frac{16}{3}$ sq. units
$\frac{19}{3}$ sq. units
Solution
$\begin{aligned} A &=\int_{1}^{2}\left(x^{2}+1\right) d x \\ &=\left[\frac{x^{3}}{3}+x\right]_{1}^{2}=\left(\frac{8}{3}+2\right)-\left(\frac{1}{3}+1\right)=\frac{10}{3} \end{aligned}$
