MHT CET · Maths · Area Under Curves
The area of the region bounded by the curve \(y^2=9 x\) and the line \(y=3 x\) is
- A \(\frac{3}{2}\) sq.units
- B 1 sq.units
- C \(\frac{1}{2}\) sq.units
- D \(\frac{1}{4}\) sq.units
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\) sq.units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Required area }=\int_0^1(3 \sqrt{x}-3 x) d x \\ & =3\left[\frac{2}{3} x^{3 / 2}-\frac{x^2}{2}\right]_0^1 \\ & =3\left(\frac{2}{3}-\frac{1}{2}\right) \\ & =3 \times \frac{1}{6}=\frac{1}{2}\end{aligned}\)
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