Find the mass of the cylinder , if the density at the point is .

I think we should use the cylincal polar method to do this, however i have problem converting this into the polar form, which is , ,

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- Jan 31st 2011, 02:50 PMwopashuiFind the mass of the cylinder
Find the mass of the cylinder , if the density at the point is .

I think we should use the cylincal polar method to do this, however i have problem converting this into the polar form, which is , , - Jan 31st 2011, 03:36 PMAckbeet
You're having trouble converting the integrand into cylindrical coordinates? What happens when you plug in for x and y?

- Jan 31st 2011, 03:52 PMHallsofIvy
You might find this trig identity helpful:

.

Perhaps you will remember the more basic identity

cos(a+ b)= cos(a)cos(b)- sin(a)sin(b).

Let a= b= x. - Jan 31st 2011, 06:48 PMwopashui
- Feb 1st 2011, 01:07 AMAckbeet
No, I don't think you've quite got it yet. Just plugging in gives:

You see how I work here: step-by-step. I don't often skip steps.

The other thing you have to worry about is that the volume differential in cylindrical components is not just

So, putting this all together, what does your integral look like now? - Feb 1st 2011, 08:32 AMwopashui
- Feb 1st 2011, 08:35 AMAckbeet
Yes. The condition with no explicit limits on the angle, implies that

- Feb 2nd 2011, 10:34 AMwopashui
- Feb 2nd 2011, 10:47 AMAckbeet
Show your work, and I'll take a look.