Example 4 on http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx
Why is this correct? How does subtracting the volume under z = 16 from the volume under z = x^2 + y^2 on a specific radius give us the desired volume?

Question

anonymous · Answer

Sorry dude the link doesn't work....

anonymous · Answer

Is this Calc 3?

anonymous · Answer

Sorry, I fixed it now. Yes it is.

anonymous · Answer

Wow... I am sorry I can't help. I just started Calculus - I am only in tenth grade. Sorry.

anonymous · Answer

No problem :)

irishboy123 · Answer

you're looking for the volume of the paraboloid itself, ie the volume inside that solid

but the normal double integral of the function f, ie$ \iint f(x,y) \ dA $ will give you the volume under the pataboloid, ie the volume from the xy plane upwards

irishboy123 · Answer

handily, though, that volume it does give you can be subtracted from the volume of the cylinder to get the inside volume.

and by cylinder i mean the volume under the plane $z = 16$ within the region $16 = x^2 + y^2$

phi · Answer

In 2D they are doing this
|dw:1440248565912:dw|
that is the integral under the curve f(x)