Answer
$A=\frac{8\pi}{3}$
Work Step by Step
Formula is $A= \int\pi(f(x)^{2})-g(x)^{2})dx$
a= 0, b=4
$f(x)=\sqrt x$
$g(x)=\frac{1}{2}x$
$A= \int\pi((\sqrt x)^{2}-(\frac{1}{2}x)^{2})dx$
$= \int\pi(x)-(\frac{x^2}{4}))dx$
$=\pi( \frac{x^2}{2}-\frac{x^3}{3*4})|4,0$
$=\frac{\pi*4^2}{2}-\frac{\pi*4^3}{12}-\frac{\pi*0^2}{2}-\frac{\pi*0^2}{12}$
$=\pi*8-\frac{\pi*64}{12}-0$
$=\pi*8-\frac{\pi*16}{3}$ due to common factor of 4
$=\frac{8\pi}{3}$
