# Applied Mathematics/Complex Integration

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## Complex integration[edit]

On the piecewise smooth curve , suppose the function *f(z)* is continuous. Then we obtain the equation below.

where is the complex function, and is the complex variable.

## Proof[edit]

Let

Then

The right side of the equation is the real integral, therefore, according to calculus, the relationship below can be applied.

Hence

This completes the proof.