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How to change the order of variable upper bound integral and repeated integral in integrand function
The double integral is a principal integral;

Iterative integration is a technical integration.

Integral in principle is just a principle. Whether it can be integrated or not, it usually becomes repeated integration.

Only in special cases, double integrals do not need to be converted into repeated integrals, for example, in electrostatics.

If it is applied to the special symmetry of Gauss theorem, it can be achieved in one step, which is a special case.

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The specific process is:

1, first draw according to the integral area;

2. Then consider how to arrange the order, and the integration process will become simple.

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Please refer to the following picture examples, each picture can be clicked to enlarge;

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