The area of the region R = (x,y) : 5x^2 y 2x^2+9 is:

Question

The area of the region $R = \{(x,y) : 5x^2 \le y \le 2x^2+9\}$ is:

Accepted Answer

$5x^2=2x^2+9 \Rightarrow x^2=3 \Rightarrow x=\pm\sqrt3$.

$$\text{Area} = \int_{-\sqrt3}^{\sqrt3}\left(2x^2+9-5x^2\right)dx = 2\int_0^{\sqrt3}(9-3x^2)\,dx = 2\left[9x-x^3\right]_0^{\sqrt3} = 2(9\sqrt3-3\sqrt3) = 12\sqrt3$$

Solutions · 1