Reduction Formulae for Trigonometric Functions

Integral calculus is more important in many areas of day to day life, like finding areas of irregular plane regions, length of curves, volume, surface area of solid of revolution, mass, moment of inertia, centre of gravity etc.

In the solution of many physical or engineering problems, we have to integrate some integrands involving powers or products of trigonometric functions. In this unit we shall devise a quicker method for evaluating these integrals.We shall consider some standard forms of integrands one by one, and derive formulas to integrate them.

Reduction formulae connects an integral with another integral of lower order, which help us to evaluate the given integral. Reduction formulae reduces a given integral to a known integration form by the repeated application of integration by parts. In this module we will cover only the reduction formulae for trigonometric functions.

The integrands which we will discuss here have one thing in common. They depend upon an integer parameter. By using the method of integration by parts we shall try to express such an integral in terms of another similar integral with a lower value of the parameter. You will see that by the repeated use of this technique, we shall be able to evaluate the given integral.