The area (in sq.

Question

The area (in sq. units) of the region enclosed by the curves $y=x^2-1$ and $y=1-x^2$ is equal to:

Accepted Answer

$x^2-1=1-x^2 \Rightarrow x=\pm1$.

$$\text{Area} = \int_{-1}^1\left[(1-x^2)-(x^2-1)\right]dx = 2\int_0^1(2-2x^2)\,dx = 4\left[x-\frac{x^3}{3}\right]_0^1 = 4\cdot\frac23 = \frac83$$

Solutions · 1