Thread: Multiple variable integration using polar coordinates: Quick question

Hello folks,

I have a quick - and probably stupid - question regarding this particular method of integrating multiple variable functions. The volume of the region given by the formula goes until and stops at the oXY plane, right?

Let's say I want the volume of a unit sphere. I would then have to multiply the by 2, correct?

Thanks!

Yes, you are correct.

The upper half of a unit sphere is defined by the function



In finding the volume of the upper half of a unit sphere (say, for ), we would integrate this function in its circular domain and multiply by two.

Originally Posted by Scott H

Yes, you are correct.

The upper half of a unit sphere is defined by the function



In finding the volume of the upper half of a unit sphere (say, for ), we would integrate this function in its circular domain and multiply by two.

I believe that it would be (with the center at the origin)

or for the top half

Originally Posted by Pierre-Alexandre

Hello folks,

I have a quick - and probably stupid - question regarding this particular method of integrating multiple variable functions. The volume of the region given by the formula goes until and stops at the oXY plane, right?

I don't know what you mean by that.

Let's say I want the volume of a unit sphere. I would then have to multiply the by 2, correct?

Thanks!

The unit sphere is given by or . is the upper half of the sphere so, by symmetry, you could get the volume of the sphere by integrating 2 times that. I don't know where you got or what "C" is.