The area (in square units) of the region bounded by the curves y+2x^2=0 and y+3x^2=1 is eq…

Question

The area (in square units) of the region bounded by the curves $y+2x^2=0$ and $y+3x^2=1$ is equal to:

Accepted Answer

$y=-2x^2$ and $y=1-3x^2$ meet where $-2x^2=1-3x^2 \Rightarrow x^2=1 \Rightarrow x=\pm1$.

$$\text{Area} = \int_{-1}^1\left[(1-3x^2)-(-2x^2)\right]dx = \int_{-1}^1(1-x^2)\,dx = \left[x-\frac{x^3}{3}\right]_{-1}^1 = \frac43$$

Solutions · 1