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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 is an integral of an integral of f(x, y). It is evaluated in two stages. First evaluate the inside integral by ordinary definite integration, treating x as a constant. This gives us a function of x alone. Second, evaluate the outside integral by a second definite integration. We shall usually drop the brackets around the inside integral and write the iterated integral as


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