Question

The area (in sq. units) of the region bounded by the parabola, $y=x^2+2$ and the lines $y=x+1,x=0$ and $x=3,$ is:

• A. $\frac{15}{2}$
• B. $\frac{21}{2}$
• C. $\frac{17}{4}$
• D. $\frac{15}{4}$

Answer 1

The correct option is A $\frac{15}{2}$


Area of the shaded region
$=\underset{0}{\overset{3}{\int }}(x^2+2)dx-\underset{0}{\overset{3}{\int }}(x+1)dx$
$={[\frac{x^3}{3}+2x]}_0^3-{[\frac{x^2}{2}+x]}_0^3$
$=(9+6-0-0)-(\frac{9}{2}+3-0)$
$=\frac{15}{2}$ sq. units