I got it wrong . . . why?
\(\displaystyle \displaystyle V \:=\: 2\pi\int^3_0 r\!\cdot\!h\, dx\)
where \(\displaystyle r = x,\;h = 18-y\)
\(\displaystyle \displaystyle V \:=\: 2\pi \int^3_0 x(18-6x)\,dx \;=\;2\pi\int^3_0(18x - 6x^2)\, dx \)
. . \(\displaystyle =\;2\pi(9x^2 - 2x^3)\,\bigg]^3_0 \;=\; 2\pi (27-18) \;=\; 18\pi\)
. . . . . . . . . . . . . . . . . . . . . . . . . .\(\displaystyle \uparrow\)
. . . . . . . . . . . . . . . . . . . . . . . . .Here!
