Multiple integral

The multiple integral is a definite integral of a function of more than one real variable, for example, or .

Integrals of a function of two variables over a region in are called double integrals, and integrals of a function of three variables over a region of are called triple integrals.

Here we only talk about double integrals.


  1. Thinking an object which upper body is an wave, and its lower body is an squre. The x axis face you. The wave function is
  2. Now put your knife down right through its center, what you will get is a slice of bread
  3. We should calculates the area of that slice: , undefined(so many) lines come together with y direction to a slice
  4. Then undefined(so many) slices come together with x direction to an complete object:

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