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MATH
[1251]

Methods from Change of variables and polar coordinates

All methods from Change of variables and polar coordinates.

Back to Change of variables and polar coordinates

Choose and apply a coordinate change

To change variables in a double integral:

  1. choose new coordinates suggested by the boundaries or by a repeated expression in the integrand;
  2. solve for xx and yy in terms of the new coordinates when needed;
  3. transform every boundary of the region;
  4. rewrite the integrand;
  5. calculate the absolute Jacobian factor;
  6. integrate over the transformed region.

Good coordinates simplify the region, the integrand or both. A substitution that simplifies the formula but complicates the region may not help.

  1. [1]:Change of variables
  2. [2]:A linear change of variables
  3. [3]:A nonlinear change of variables
  4. [4]:Changing variables in an elliptical integral

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Choose and apply a coordinate change