The area of the region bounded by the line $y=3 x$ and the curve $y=x^2$ sq units is

• A

  $10$
• Correct answer
  B

  $9 / 2$
• C

  $9$
• D

  $5$

Solution

We have, $y=3 x$ and $y=x^2 \Rightarrow 3 x=x^2$ $x=3$ and $x=0$ are the points of intersection.
Now, area $=\int_0^3\left(3 x-x^2\right) d x$ $=\left.\frac{3 x^2}{2}\right|_0 ^3-\left.\frac{x^3}{3}\right|_0 ^3$ $=3 \cdot \frac{9}{2}-\frac{27}{3}$ $=\frac{27}{2}-9=\frac{9}{2}$ sq units

Hence, the correct answer is option: 'B'.