The area (in sq. units) of the region bounded

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 :

  1. $\frac{15}{4}$

  2. $\frac{15}{2}$

  3. $\frac{21}{2}$

  4. $\frac{17}{4}$


Correct Option: , 2

Solution:

Req. area $=\int_{0}^{3}\left(\mathrm{x}^{2}+2\right) \mathrm{dx}-\frac{1}{2} \cdot 5 \cdot 3=9+6-\frac{15}{2}=\frac{15}{2}$

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