Question

Find the area of the closed figure bounded by the following curve
$y=1+x^2,y=2$.

Answer 1

$y=2,y=1+x^2$

$2=1+x^2\Rightarrow x=\pm 1$

Area enclosed between $x=1andx=-1isequalto{\int }_{-1}^1(2-(1+x^2\left)\right)dx$

$=[x-\frac{x^3}{3}{]}_{-1}^1=2-\frac{2}{3}=\frac{4}{3}$