Question

The area of the region (rounded off to one decimal place) enclosed between the curves $y = x$ and $y = 3\sqrt{x}$ and between the lines $x = 0$ and $x = 1$ is ____________ units

Hint:

Always integrate (upper curve – lower curve) to find area.

Answer 1

Correct Answer: 1.5

Area:
\[ A = \int_{0}^{1} (3\sqrt{x} - x)\, dx. \]
Compute:
\[ \int 3\sqrt{x}\, dx = 2, \qquad \int x\, dx = \frac{1}{2}. \]
Thus:
\[ A = 2 - \frac{1}{2} = 1.5. \]
\[ \boxed{1.5} \]