anonymous
  • anonymous
find the volume of the solid obtained by rotating about the y-axis the region bounded by the curve y=2x^2-x^3 and the x-axis. How do I do this?
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
find the the x and y intercepts
anonymous
  • anonymous
ok.
amistre64
  • amistre64
y = x^2(2-3x) right?

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amistre64
  • amistre64
y=0 at 0 and 3/2 right?
anonymous
  • anonymous
no y=x^2(2-x)
amistre64
  • amistre64
thats right lol.... i transposed that 3 dint i :)
amistre64
  • amistre64
so we have bounds of x=0 and x=2 then right?
anonymous
  • anonymous
yes.
amistre64
  • amistre64
we need to get these in terms of y to calculate the y axis spin; lets do an inverse
anonymous
  • anonymous
ok sounds good.
amistre64
  • amistre64
x = 2y^2 -y^3 ; solve for y :)
amistre64
  • amistre64
wolfram might help with this :)
anonymous
  • anonymous
good idea. I will get back to you a little later on this I have a baseball game.
amistre64
  • amistre64
are you sure its spun around the y axis? and not the x axis?
amistre64
  • amistre64
let me read up on the shell method; its prolly easier with this setup..
amistre64
  • amistre64
2pi [S] x[f(x)] dx ; from [0,2]
amistre64
  • amistre64
x(2x^2-x^3) = 2x^3 -x^4 soo... we integrate that to get; (5x^4 -2x^5)/10. At 0 it is zero; so we just worry about the 2
amistre64
  • amistre64
i get 8/5 as the volume of the torus....if i did it right lol
amistre64
  • amistre64
so i am going to try this on firefox..... and it seems to be working good so far :)

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