This is the area to be rotated around the x-axis:


The graph of `y=x`, with the area under the "curve" between `x=0` to `x=2` shaded.

Hence, the volume generated can be found using the formula for volume of solid of revolution:

`"Vol" = pi int_a^b y^2 dx`

`=pi int_0^2 (x)^2 dx`

`= pi[(x^3)/(3)]_0^2`


`=8/3 pi\ text[units]^3`

`~~8.378\ text[units]^3`

Get the Daily Math Tweet!
IntMath on Twitter