MHT CET · Maths · Area Under Curves
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
- A 36
- B 18
- C \(\frac{27}{4}\)
- D 9
Answer & Solution
Correct Answer
(D) 9
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Required area } & =\int_0^9 \sqrt{x} \mathrm{~d} x-\int_3^9\left(\frac{x-3}{2}\right) \mathrm{d} x \\ & =\left[\frac{2 x^{3 / 2}}{3}\right]_0^9-\frac{1}{2}\left[\frac{x^2}{2}-3 x\right]_3^9 \\ & =\frac{2}{3}(27-0)-\frac{1}{2}(36-18) \\ & =9 \text { sq.units }\end{aligned}\)
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