Setting up limits for a triple integral in cylindrical coordinates

norbellys · Jul 17, 2016

1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

Homework Equations

The Attempt at a Solution

Handwritten notes on lined paper: a triple integral setup in Cartesian form with limits from -R to R, then cylindrical coordinate substitutions x = r cos θ, y = r sin θ, z = z, and rewritten limits, followed by a re-expressed integral over θ from 0 to 2π, r from 0 to R, with integrand r^2 sqrt(R^2 - r^2).

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LCKurtz · Jul 17, 2016

norbellys said:

1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

Homework Equations
The Attempt at a Solution

[/B]

Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.

norbellys · Jul 18, 2016

LCKurtz said:

Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.

yes that was what I was missing !

Setting up limits for a triple integral in cylindrical coordinates

Homework Equations

The Attempt at a Solution

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Homework Equations

The Attempt at a Solution

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