Piecewise integration can be used to obtain the **reduction formulas** for integrals.

These formulas express an integral with function power in terms of an integral that involves a lower power of that function.

For example, if * no* is a positive integer and * no* 2, then piecewise integration can be used to obtain the reduction formulas.

(2)

To illustrate how these formulas are obtained, let us deduce formula (2).

for what

Transposing the last term to the left side gives

of which one has (2).

**Example**

Calculate

** Solution. **From (2), with

*no*=4