The area of the region enclosed between the parabolas y2=2x−1 and y2=4x−3 is:
Solutions · 1
Official solution
The parabolas meet where 2x−1=4x−3⇒x=1,y=±1.
\[\text{Area}=\int_{-1}^1\left[\frac{y^2+3}4-\frac{y^2+1}2\right]dy=\int_{-1}^1\frac{1-y^2}4\,dy=\frac14\left[y-\frac{y^3}3\right]_{-1}^1=\frac14\cdot\frac43=\frac13.\]