Question

Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0,
y= 5+x^7, about the y-axis.

Answer 1

\[\int\limits_{a}^{b}2\pi x f(x)dx\]

Answer 2

@Zarkon , how do you account for removal of graph below x -axis.

Answer 3

Use shell method...
\[Volume = 2\pi \int_{0}^{1} x(5+x^7) dx = 2\pi \int_{0}^{1} (5x+x^8) dx = 2\pi [5/2(x^2) +(1/9)x^9]_{0}^{1} = (47/9)\pi\]

Answer 4

@Callisto , same question to you as to Zarkon .

Answer 5

I think you you should divide the final answer by 2

Answer 6

http://en.wikipedia.org/wiki/Shell_integration

Answer 7

Length of the shell = f(x)
width of the shell = 2pi x
thickness of the shell = (delta) x
Volume = area x thickness = 2pi int x(f(x) dx