Converting to Polar Coordinates

[eckothegecko]

When working out a double integral in polar coordinates do you need to put in the r part of the r dr d(theta) if there is already an r in the equation you are trying to integrate?

Example

Integral of cr dr d(theta) or integral of cr r dr d(theta)? Where cr is the equation being integrated?

Thanks

 

[Ishuda]

When working out a double integral in polar coordinates do you need to put in the r part of the r dr d(theta) if there is already an r in the equation you are trying to integrate?

Example

Integral of cr dr d(theta) or integral of cr r dr d(theta)? Where cr is the equation being integrated?

Thanks

The answer depends on whether you initially have an integral in cartesian co-ordinates or not. If you are converting from cartesian co-ordinates and the function converted to cr, then yes you need to put in the r part of the
r dr d\(\displaystyle \theta\) also.

 

[HallsofIvy]

The "differential of area" in Cartesian coordinates is \(\displaystyle dxdy\). In polar coordinates, the differential of area is \(\displaystyle r drd\theta\). If your integral has "\(\displaystyle dxdy\)" then, yes, you need to change that to "\(\displaystyle r drd\theta\)".