Find the volume of' the solid formed by revolving the region bounded by the graph of f(x)=-x^(2)+2x and the x-axis about the x-axis...

Question

amistre64 · Answer

you will want your x intercepts as your limits of integration

anonymous · Answer

I want to check my ans...my ans is $$\frac{ -304pi }{ 15 }$$

amistre64 · Answer

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amistre64 · Answer

when doing rotations about an axis, you most likely want to use the sum of areas of a circle:  pi r^2, from a to b;  where r = f(x)$$\int_{a}^{b}\pi[f(x)]^2~dx$$

amistre64 · Answer

and volume is never negative

amistre64 · Answer

since your x intercepts are 0 and 2$$\int_{0}^{2}\pi[-x^2+2x]^2~dx$$
$$\int_{0}^{2}\pi(x^4-4x^3+4x^2)~dx$$

amistre64 · Answer

if i did it right on the paper .... 14/3 pi

amistre64 · Answer

i messed up the adding :)

amistre64 · Answer

16/15  pi

anonymous · Answer

I forget a step...haha the correct ans is 16/15 pi ~
thank you, you answer my question very detail...
I know something new too~^^