Reduction Formulae for Trigonometric Functions

Name: Reduction Formulae for Trigonometric Functions
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Trigonometric fucntions

Created byShital D. Solanki

Last updated 5/2022

English

What you'll learn

Students will learn various reduction formulae of integration
Students will be able to solve the problems involving reduction formulae
Students will be able to identify which formula to use for a specific problem
Students will be able to learn Error function and its properties

Course content

3 sections • 11 lectures • 1h 22m total length

Introduction0:25

Reduction Formula-16:28
Explore the first reduction formula for the integral of sin^n x, derived via integration by parts, showing I_n = - cos x sin^{n-1} x / n + (n-1)/n I_{n-2}.
Reduction Formula-26:56
Derives reduction formula 2 for trigonometric integrals using integration by parts. Expresses I_n in terms of I_{n-1} and I_{n-2} with cos x and sin x.
Examples on Reduction Formula-1 and 219:22
Apply reduction formulas to sine integrals, derive I_n relations, and solve even and odd cases in definite integrals using recursive steps.
Quiz on Reduction Formula-1 and 2
Reduction Formula-3 with example6:02
Explore reduction formula 3 for trigonometric integrals, prove the recurrence, and demonstrate a worked example using induction and substitution to relate I_n to I_{n-2}.
Reduction Formula-4 with examples6:45
Learn the fourth reduction formula for trigonometric integrals, prove it via substitution, and apply it through a worked example.
Reduction Formula-55:36
This lecture explains the reduction formula for trigonometric integrals, proves reduction formula-5, and demonstrates applying it to compute integrals using standard integration steps.
Reduction Formula-66:23
Examine reduction formula six for trigonometric functions integration, prove the formula, and manipulate integrals to express higher-order terms in terms of lower ones.
Examples on Reduction formula 5 and 67:53
Explore reduction formulae for trig functions with examples on formulas 5 and 6, showing how to evaluate integrals using these reduction rules.
Reduction Formula -711:49
demonstrates and proves the reduction formula for sin^m x integrals, using integration by parts and substitution to derive a relation between I_m and I_{m-2}.

Requirements

Basic knowledge of integration is required while taking up this course.

Description

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

Reduction Formulae for Trigonometric Functions

What you'll learn

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Course content

Introduction1 lecture • 1min