Double integrals
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Evaluation of a double integral
Equations are omitted for technical reasons - download the original pdf
Let the boundary of the region R be divided in such a way that the following inequalities hold [Equation goes here - download the original pdf to see it.] The function [Equation goes here - download the original pdf to see it.] is a function describing the lower boundary of the region, and the function [Equation goes here - download the original pdf to see it.] describes the upper boundary. [Diagram goes here - download the original pdf to see it.] then the integral can be evaluated as [Equation goes here - download the original pdf to see it.] In this formula the inner integral, [Equation goes here - download the original pdf to see it.] , is evaluated first by keeping x constant; the result is then integrated over x from a to b. [Example goes here - download the original pdf to see it.] The integral may also be evaluated in the other sense, by integrating over x first and then y. That is, when [Equation goes here - download the original pdf to see it.] [Equation goes here - download the original pdf to see it.]
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Contents of
Double integrals
1 Double integral
2 Evaluation of a double integral
3 Some applications double integrals
4 Change of variables
5 The double integral in polar coordinates
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