Reduction Formulae for Trigonometric Functions
- Basic knowledge of integration is required while taking up this course.
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.
Who this course is for:
- This intended for Engineering students
Her core interest areas include Graph theory, Operations Research, Real Analysis and Algebra. She has attended National level workshop on ‘Applications of Mathematics in Engineering Education‘ conducted at IIT Guwahati, attended two National Conferences on ‘Emerging trends in Soft Computing‘ and on ‘Discrete Mathematics’ and National Seminar on ‘Applications of Mathematics and Statistics in Life Sciences‘.