Consider the double integral ${\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{2x}{}}}f(x,y)dydx.$ Suppose that the function $f$ is such that switching thE order of integration makes double integral more convenient to integrate.

Which of the following double integrals is equivalent to the given double integral?

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

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

${\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{\frac{1}{2}y}{}}}f(x,y)dxdy$

${\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{\frac{1}{2}y}{\overset{2}{}}}f(x,y)dxdy$