Question

The area of the region enclosed by the curve $y = \sqrt{x}$ and the lines $x = 0$ and $x = 4$ and the x-axis is :

• A. $\frac{16}{9}$ sq. units
• B. $\frac{32}{9}$ sq. units
• C. $\frac{16}{3}$ sq. units
• D. $32$ sq. units

Hint:

To find the area under a curve, set up the integral of the function over the given interval and evaluate it.

Answer 1

The Correct Option is C

The area under the curve $y = \sqrt{x}$ from $x = 0$ to $x = 4$ is given by the integral: \[ A = \int_0^4 \sqrt{x} \, dx \] Evaluating this integral: \[ A = \int_0^4 x^{1/2} \, dx = \left[ \frac{2}{3} x^{3/2} \right]_0^4 = \frac{2}{3} (4^{3/2}) = \frac{2}{3} (8) = \frac{16}{3} \] Thus, the area is $\frac{16}{3}$ sq. units.