Reduction Formula Evaluation of Integrals: Integral Calculus

Integration by Successive Reduction

Created byAlok Gupta

Last updated 5/2020

Hindi

What you'll learn

Reduction Formula
Integration techniques, Integration by successive reduction,
gamma function and its application in evaluating the complex integrals
Integration of trigonometric functions of higher degree
solving complicated integrals

Course content

10 sections • 21 lectures • 1h 48m total length

What is Reduction Formula?4:59
Integration by Parts8:17
Introduction to Definite Integrals4:09

Reduction formula for sin^n x6:32
Here, you will learn to derive the Reduction formula for the integral of sin^n x with respect to x using product rule of integration.
Reduction formula for sin^m x cos^n x9:06
You will learn to derive the reduction formula for the integral of sin^m x cos^n x. you may observed that the power m is remaining same but the power of n is reduced to n-2.
Shortcut method to evaluate the integral of sin^m x cos^n x.9:16
This is an alternative way or shortcut method to evaluate the integral of sin^m x cos^n x by using simple application of the derivatives. Moreover, the connection between the two integrals is easily established.

Requirements

Basics of Integration specially integration by parts
be able to solve simple integrals based on trigonometric functions

Description

You have noticed somewhere that any formula which connects the given integral with another integral in which the integrand is of the same type but is of lower degree is called a Reduction Formula. Repeated or continuous application of reduction formula helps us to evaluate the given integral. This method of integration is called integration by successive reduction. Reduction formula can be easily derived using integration by parts i.e., product rule of integration. In this whole course, assume n, m are to be integers unless, otherwise stated.

Who this course is for:

Undergraduate and Post Graduate students
Bsc students, B tech students
Any student who wants to master various integration techniques

Reduction Formula Evaluation of Integrals: Integral Calculus

What you'll learn

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Course content

About the Course3 lectures • 17min

Reduction Formula for the Integral of (i) sin^n x (ii) cos^n x3 lectures • 25min

Gamma Function and its Application in Reduction Formula: Walli's formula3 lectures • 13min

Definite integral of sin^m x cos^n x from 0 to pi/2 using Walli's formula4 lectures • 6min

Reduction formula for tan^n x and cot^n x1 lecture • 3min

Reduction formula for sec^n x and cosec^n x1 lecture • 5min

Integral of cos^m x sin nx, cos^m x cos nx, sin^m x cos nx, sin^m x sin nx1 lecture • 8min

Integral of x^n sin mx, x^n cos mx, x sin^n x, x cos^n x2 lectures • 10min

Reduction formula for e^ax sin^n bx, e^ax cos^n bx, x^n sin bx, x^n cos bx2 lectures • 11min

Reduction Formula for the integral of x^m (a+bx^n)^p1 lecture • 11min

Requirements

Description

Who this course is for: