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 :
Correct Option: , 4
Solution:
Area of the bounded region $\int_{0}^{3}\left[\left(x^{2}+2\right)-(x+1)\right] d x$
$=\left[\frac{x^{3}}{3}-\frac{x^{2}}{2}+x\right]_{0}^{3}$
$=9-\frac{9}{2}+3=\frac{15}{2}$
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