The area (in sq. units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0$, $\mathrm{X}$-axis and lying in the…

The area (in sq. units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0$, $\mathrm{X}$-axis and lying in the first quadrant, is
  1. 6
  2. $\frac{27}{4}$
  3. 9
  4. 18

Solution

$\begin{aligned} & \int_0^9 \sqrt{x} \mathrm{~d} x-\frac{1}{2} \times 6 \times 3 \\ & =\frac{2}{3}\left[x^{3 / 2}\right]_0^9-9\end{aligned}$ $=\frac{2}{3} \times 27-9=9$

Asked in: MHT CET 2022 (10 Aug Shift 2)

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