Area Question 9
Question 9
- 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
(2019 Main, 12 Jan I) (a) $\frac{15}{2}$ (b) $\frac{17}{4}$ (c) $\frac{21}{2}$ (d) $\frac{15}{4}$
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Solution:
- Given equation of parabola is $y=x^{2}+2$, and the line is $y=x+1$
The required area $=$ area of shaded region $=\int_{0}^{3}\left(\left(x^{2}+2\right)-(x+1)\right) d x=\int_{0}^{3}\left(x^{2}-x+1\right) d x$
$=\frac{x^{3}}{3}-\frac{x^{2}}{2}+x^{3}=\frac{27}{3}-\frac{9}{2}+3-0$
$=9-\frac{9}{2}+3=12-\frac{9}{2}=\frac{15}{2}$ sq units
