Question

The area of the region enclosed between the parabolas $y^2=2x-1$ and $y^2=4x-3$ is

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

Required area $=2\underset{0}{\overset{1}{\int }}\left(\frac{y^2+3}{4}-\frac{y^2+1}{2}\right)dy$
$=2\underset{0}{\overset{1}{\int }}\frac{1-y^2}{4}dy=\frac{1}{2}{\left|y-\frac{y^3}{3}\right|}_0^1=\frac{1}{3}$