in a RxRxRxR; what is the volume of rotation of the equation: y = 2x+7z^2-4w^2+9; from 0 to 2 in all directions. Rotated about the y axis?

Question

in a RxRxRxR; what is the volume of rotation of the equation: y = 2x+7z^2-4w^2+9; from 0 to 2 in all directions.  Rotated about the y axis?

anonymous · Answer

what is a RxRxRxR?  a hypercube?

amistre64 · Answer

its a hyperspace, yes.  if thats the proper term :)

anonymous · Answer

y=14z^(2)-8w^(2)+2x+9, I am not sure on this answer but looks right.......

anonymous · Answer

is it right?

anonymous · Answer

hyperspace? Wow, Star Trek is getting closer to reality.

try using integration

amistre64 · Answer

that looks closer to a derivative than a volume of revolution.

anonymous · Answer

I tried

amistre64 · Answer

you did :)  and thats good

amistre64 · Answer

im curious if i would use the shell method or not :)

anonymous · Answer

I like the plate method

amistre64 · Answer

so what is the equation for volume in hyperspace?  im sure its the integration of volume; since  area ups to volume

anonymous · Answer

it's.... a double integral?

amistre64 · Answer

$$\int 2pi\ r\ dr=pi\ r^2$$
$$\int pi\ r^2\ dr=\frac{pi}{3}\ r^3$$

amistre64 · Answer

what it is?  i got no idea yet :)