If $R=\{(x,y)$:$x^{2}y4,0x2\},$ then ${}_{R}f(x,y)dA$ equals

$($a$){\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{y}}{}}}f(x,y)dxdy.$

$($b$){\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{x^2}{}}}f(x,y)dxdy.$

$($c$){\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{x^2}{}}}f(x,y)dydx.$