We investigate a small piece of area in a 2D region. We justify pictorially, the factor of r in the form dA = r dr theta. The Jacobian determinant is given for circular polars, which is then shown to yield r as the appropriate factor in the area dA.

The small element of area for circular polar coordinates (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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The small element of area for circular polar coordinates (MathsCasts)

The small element of area for circular polar coordinates (MathsCasts)