Which of the following is the correct equation to find the area of the shaded region, with reference to the figure given below?

$A=2 \int\limits_0^8\left(2 x-x^2\right) d x$ $A=2 \int\limits_0^4\left(2 x-x^2\right) d x$ $A=2 \int\limits_0^4\left(2 x-\frac{x^2}{4}\right) d x$ $A=\int\limits_0^8\left(2 x-\frac{x^2}{4}\right) d x$

$A=\int\limits_0^8\left(2 x-\frac{x^2}{4}\right) d x$

from given figure x values from 0 to 8 so to find area as y = 2x is above $x^2=4y$ so  Ar(y = 2x) along x-axis - Ar(x2 = 4y) along x-axis = Net area $=\int\limits_0^8  2 x-\frac{x^2}{4} d x$