hi all
suppose I have a solid like y=1-x^2 and y=0 rotated about x.
if i cut disks parallel to x, each disk has a radius of its x co-ordinate and a thickness of del y
summings those disks across the y in which they exist should have the integral
V = int{-1,1}pi(x)^2 dy
or
V = int{-1,1}pi((1-y)^1/2)^2 dy
if i cut disks parallel to y axis the have radius of the y co-ordinate and thickness of del x
v=int{-1,1}pi(y)^2 dx
or
v=int{-1,1}pi(1-x^2)^2 dx
why am I getting two different volumes? conceptually i dont understand...am i not still summing individual disks across a region?
thanks!
suppose I have a solid like y=1-x^2 and y=0 rotated about x.
if i cut disks parallel to x, each disk has a radius of its x co-ordinate and a thickness of del y
summings those disks across the y in which they exist should have the integral
V = int{-1,1}pi(x)^2 dy
or
V = int{-1,1}pi((1-y)^1/2)^2 dy
if i cut disks parallel to y axis the have radius of the y co-ordinate and thickness of del x
v=int{-1,1}pi(y)^2 dx
or
v=int{-1,1}pi(1-x^2)^2 dx
why am I getting two different volumes? conceptually i dont understand...am i not still summing individual disks across a region?
thanks!