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Iterated Integral

In this section we shall learn how to evaluate double integrals. A double integral can be evaluated by two single integrations. The Iterated Integral Theorem gives the key formula.

The iterated integral

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is an integral of an integral of f(x, y). It is evaluated in two stages. First evaluate the inside integral

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by ordinary definite integration, treating x as a constant. This gives us a function of x alone. Second, evaluate the outside integral

12_multiple_integrals-70.gif

by a second definite integration.

We shall usually drop the brackets around the inside integral and write the iterated integral as

12_multiple_integrals-71.gif


Last Update: 2006-11-25