Question

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?

Answer 1

find the the x and y intercepts

Answer 2

ok.

Answer 3

y = x^2(2-3x) right?

Answer 4

y=0 at 0 and 3/2 right?

Answer 5

no y=x^2(2-x)

Answer 6

thats right lol.... i transposed that 3 dint i :)

Answer 7

so we have bounds of x=0 and x=2 then right?

Answer 8

yes.

Answer 9

we need to get these in terms of y to calculate the y axis spin; lets do an inverse

Answer 10

ok sounds good.

Answer 11

x = 2y^2 -y^3 ; solve for y :)

Answer 12

wolfram might help with this :)

Answer 13

good idea. I will get back to you a little later on this I have a baseball game.

Answer 14

are you sure its spun around the y axis? and not the x axis?

Answer 15

let me read up on the shell method; its prolly easier with this setup..

Answer 16

2pi [S] x[f(x)] dx ; from [0,2]

Answer 17

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

Answer 18

i get 8/5 as the volume of the torus....if i did it right lol

Answer 19

so i am going to try this on firefox..... and it seems to be working good so far :)