Question

Find area bounded by the curves $x^2\le y\le x+2$.

• A. $\frac{11}{2}$
• B. $\frac{7}{2}$
• C. $\frac{9}{2}$
• D. $\frac{5}{2}$

Answer 1

The correct option is C $\frac{9}{2}$

$x^2\le y\le x+2$
$x^2=x+2$
$\Rightarrow x=-1$ or $2$
Hence required area $={\int }_{-1}^2(x+2-x^2)dx$
$={\frac{x^2}{2}+2x-\frac{x^3}{3}|}_{-1}^2=(2+4-\frac{8}{3})-(\frac{1}{2}-2+\frac{1}{3})=\frac{10}{3}+\frac{7}{6}=\frac{27}{6}=\frac{9}{2}$.