8

Reduction Formulas

A reduction formula for a given integral is an integral which is of the same type as the given integral but of a lower degree (or order). The reduction formula is used when the given integral cannot be evaluated otherwise. The repeated application of the reduction formula helps us to evaluate the given integral. In what follows, we shall observe that the reduction formulas are obtained by repeated application of integration by parts.

8.1 REDUCTION FORMULAS FOR images AND images

(i) Integration by parts yields

 

 

Therefore, transposing ...

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