Question

The area (in sq. units) of the region $A=\left\{\right(x,y)\in R\times R|0\le x\le 3,0\le y\le 4,y\le x^2+3x\}$
is:

• A. $8$
• B. $\frac{26}{3}$
• C. $\frac{59}{6}$
• D. $\frac{53}{6}$

Answer 1

The correct option is C $\frac{59}{6}$

Given,
$y\le x^2+3x$
$0\le x\le 3$

Required region
$={\int }_0^1[x^2+3x]dx+(2\times 4)$
$={[\frac{x^3}{3}+\frac{3}{2}{x}^2]}_0^1+8$
$=\frac{2+9+48}{6}$
$=\frac{59}{6}$