What is the Volume of Revolution if the area bounded by the curve y=x^2-4x and the x-axis is is rotated about the x-axis?
1 Answer
Mar 5, 2017
(512 pi) /15 \ unit^3
Explanation:
I recommend that you always draw a sketch to clarify what needs calculating.
graph{x^2-4x [-10, 10, -5, 5]}
The curve intersects the
x^2-4x = 0 => x(x-4)=0 => x=0,4
The Volume of Revolution about
VOR = int_alpha^beta \ piy^2 \ dx
So in this case:
VOR = int_0^4 \ pi \ (x^2-4x)^2 \ dx
" " = pi \ int_0^4 \ (x^4-8x^3+16x^2) \ dx
" " = pi [ x^5/5-2x^4+16x^3/3]_0^4
" " = pi { (4^5/5-2*4^4+16*4^3/3)-(0) }
" " = pi (1024/5-512+1024/3)-(0) }
" " = (512 pi) /15