Area Ques 70
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
(2019 Main, 12 Jan I)
(a) $\frac{15}{2}$
(b) $\frac{17}{4}$
(c) $\frac{21}{2}$
(d) $\frac{15}{4}$
Show Answer
Answer:
Correct Answer: 70.(a)
Solution:
Formula:
- Given equation of parabola is $y=x^{2}+2$, and the line is $y=x+1$
The required area $=$ area of shaded region
$=\int _{0}^{3}\left(\left(x^{2}+2\right)-(x+1)\right) d x=\int _{0}^{3}\left(x^{2}-x+1\right) d x$
$=[\frac{x^{3}}{3}-\frac{x^{2}}{2}+x] _{0}^{3}=(\frac{27}{3}-\frac{9}{2}+3)-0$
$=9-\frac{9}{2}+3=12-\frac{9}{2}=\frac{15}{2}$ sq units
BETA
