Area of the region bounded by the curve $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$ is

Area of the region bounded by the curve $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$ is
  1. $\frac{19}{2}$ sq $\cdot$ units
  2. $\frac{21}{2} \mathrm{sq} \cdot$ units
  3. $15 s q \cdot$ units
  4. $\frac{9}{2} \mathrm{sq} \cdot \mathrm{units}$

Solution

$\begin{aligned} & \text { Required area }=\int_0^3\left(x^2+2-x\right) d x=\left[\frac{x^3}{3}+2 x-\frac{x^2}{2}\right]_0^3 \\ & =\frac{27}{3}+6-\frac{9}{2}=\frac{21}{2}\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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