Verified answer

http://www.wolframalpha.com/input/?i=graph+y%3D4sq...

y= 4 sqrt(x)

y = x

4 sqrt(x) = x

squate both sides

16x = x^2

x^2-16x=0

x(x-16)=0

x= 0

x= 16

Limits of integration is 0 to 16

y=16 is a horizontal line so the rotation is along the x-axis

Volume = pi ∫ ((16-x)^2 - (16-4sqrt(x))^2 ) dx

(16-x)^2 -(16-4sqrt(x))^2 = 256-32x+x^2 - 256 +128sqrt(x) -16x = x^2-48x+128sqrt(x)

Volume = pi ∫ (x^2-48x+128 sqrt(x)) dx

∫(x^2-48x-128sqrt(x) dx = (1/3)x^3 -(48/2)x^2 + (128)(2/3) x^(3/2)

= (1/3)x^3 -24x^2 -(256/3) x^(3/2)

F(x) = (1/3)x^3 -24x^2 +(256/3) x^(3/2)

F(16) = 2048/3

F(0) = 0

Volume = 2048pi/3

Answer to Find the volume formed by rotating the region enclosed by: y=4?x and y=x about the line y=16..