Question

Find thrice the area of the region bounded by the curve $y^2=2y-x$ and the y-axis.

Answer 1

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

Area of shaded region

$=-{\int }_0^2{y}^2-2ydy$

$=[\frac{y^3}{3}{]}_2^0-[y^2{]}_2^0$

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

$A=\frac{4}{3}$

$3A=4$