Question

The area (in sq unit) of the region bounded by the curves $2x=y^2-1$ and $x=0$ is

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

Answer 1

The correct option is B $\frac{2}{3}$

Given curve can be rewritten as
$y^2=2x+\frac{1}{2}$
Therefore, required area $={\int }_{-1}^{1}xdy$
$=2{\int }_0^1\frac{y^2-1}{2}dy$
$={[\frac{y^3}{3}-y]}_0^1$
$=\frac{1}{3}-1=\frac{2}{3}$ sq unit