The area (in sq.

Question

The area (in sq. units) of the region $\{x\in\mathbb R : x\ge0,\ y\ge0,\ y\ge x-2,\ y\le\sqrt x\}$ is:

Accepted Answer

$y=x-2$ meets $y=\sqrt x$ at $(4,2)$.

$$\text{Area} = \int_0^4\sqrt x\,dx - \frac12(2)(2) = \left[\frac23x^{3/2}\right]_0^4 - 2 = \frac{16}{3}-2 = \frac{10}{3}$$

Solutions · 1