Question

The area bounded by $y =x^{2} +3$ and $y =2x+3$ is

• A. $\frac{12}{7}$
• B. $\frac{4}{3}$
• C. $\frac{3}{4}$
• D. $\frac{8}{3}$
• E. $\frac{3}{8}$

Answer 1

Answer: (B)

Required area
$=\int_{0}^{2}(2 x+3)-\left(x^{2}+3\right) d x$

$=\int_{0}^{2}\left(2 x-x^{2}\right) d x$
$=\left[\frac{2 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$
$=\left[4-\frac{8}{3}\right]=\frac{4}{3}$ sq units