12-11-1xyOpen image in a new page

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

The line `y=0` simply means the `x`-axis.

From the diagram, we can see that the limits of the bounded area are x = 0 and x = 2.

The volume generated is:

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

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

`=pi int_0^2 (4x^2-4x^3+x^4) dx`

`=pi [(4x^3)/(3) - (4x^4)/(4) + (x^5)/(5)]_0^2`

`=pi [32/3 - 16 + 32/5] - pi[0]`

`=(16)/(15)pi\ text[units]^3`

`~~3.351\ text[units]^3`

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