Question

Find the area of the region bounded by curves $y=x^2+2,y=x,x=0$ and $x=3$

Answer 1

The correct answer is:$\frac{21}{2}units.$
The area bounded by the curves,$y=x^2+2,y=x,x=0,$and $x=3$,is represented by
the shaded area OCBAO as

Then,Area OCBAO=Area ODBAO-Area ODCO
$=∫^3_0(x^2+2)dx-∫^3_0xdx$
$=[\frac{x^3}{3}+2x]^3_0-[\frac{x^2}{2}]^3_0$
$=[9+6]-[\frac{9}{2}]$
$=15-\frac{9}{2}$
$=\frac{21}{2}units.$