Reduction formulae, Mathematics

Assignment Help:

 

Reduction formulae

Script for Introduction:

First let us know what is meant by reduction formula.

In simple words,

                A formula which expressess(or reduces) the integral of the nth  indexed function in terms of that of n-1th  indexed function is called a Reduction formula.

 

Let us see how reduction formula helps us in solving the problems in different cases:

 

Problem 1:

Solve  Integration of

sin4x dx

Script for this problem:

This problem can be solved by reduction formula for sine which states that,

// print line 1

 

Here we have n=4.

Therefore substituting the value  of n=4 in the given problem,we have,

//print line 2

 

Which is equal to,

//print line 3

 

On expanding  I2 in a similar manner, we can write I4 as,

//print line 4

 

Now, we know that,

//print line5

 

Which is equal to,

//print line 6

 

Here substituting the value of I0 in the equation of I4 ,we have

//print line 7

 

Thus, by reduction formula  the given problem is solved.

 


Related Discussions:- Reduction formulae

Understanding Logistics, How can i get a better understanding of logistics ...

How can i get a better understanding of logistics without having a degree on logistics and knowledge of it? Simply, in a very basic form..

Example to understanidng of multiplication, 6-year-old Rahul wasn't able to...

6-year-old Rahul wasn't able to understand multiplication when it was thrust upon him in school. His mother discussed this problem with some of us. On the basis of suggestions that

Standard deviation, 2.When investigating times required for drive-through s...

2.When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the tw

Explain the common forms of linear equations, Explain the Common Forms of L...

Explain the Common Forms of Linear Equations ? An equation whose graph is a line is called a linear equation. Here are listed some special forms of linear equations. Why should

Periodicity, how to find periods in trigon ometry

how to find periods in trigon ometry

How to calculate mode, Q. How to calculate Mode? The mode of a data set...

Q. How to calculate Mode? The mode of a data set is the value that is repeated most often in the data set. It has the highest frequency. There can be one, more than one, or n

Basic operations for complex numbers, Now we have to discuss the basic oper...

Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is

Maths Assessment, Assessment task This Term Assessment will require you ass...

Assessment task This Term Assessment will require you assess the effectiveness of your current lunch budget and prepare a proposal to your caregiver to seek permission to be given

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd