Question

Find the area bounded between the curve $y^2=2y-x$ and $y$ - axis.

• A. $5$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{4}{3}$

Answer 1

The correct option is D $\frac{4}{3}$

$y^2=2y-x$ , y-axis

$A=(0,0)$ , $B=(0,2)$

${\int }_0^{2}2y-y^{2}dx$

$=[y^2-\frac{y^3}{3}{]}_0^2$

$=4-\frac{8}{3}=\frac{4}{3}$