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MATH
[1251]

Methods from Fubini and iterated integrals

All methods from Fubini and iterated integrals.

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Choose an order of integration

To compute a double integral over a rectangle:

  1. inspect the integrand for a direct antiderivative in xx or yy;
  2. write the corresponding inner integral first;
  3. evaluate the inner integral while treating the other variable as constant;
  4. evaluate the remaining one-variable integral;
  5. use the other order as a check when it is comparably simple.

Under Fubini's hypotheses the two orders give the same value, but they need not be equally convenient.

  1. [1]:Fubini's theorem on a rectangle
  2. [2]:Computing in both orders
  3. [3]:Choosing the useful order

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Choose an order of integration