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

Logarithm functions, Logarithm Functions : In this section we'll discuss l...

Logarithm Functions : In this section we'll discuss look at a function which is related to the exponential functions we will learn logarithms in this section. Logarithms are one o

Ratio test - sequences and series, Ratio Test In this part we are goin...

Ratio Test In this part we are going to take a look at a test that we can make use to see if a series is absolutely convergent or not.  Remind that if a series is absolutely c

Credit and invoice, mr ouma bought two sets of spanners for sh 300per set ...

mr ouma bought two sets of spanners for sh 300per set two machanic vice at sh 1000each three set of screw driver at sh 115 per set and tool box for sh 300

Case let, How should Shoppers’ Stop develop its demand forecasts?

How should Shoppers’ Stop develop its demand forecasts?

Plot your data on a scatter plot, Devise data that link a certain relations...

Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT

What is a negative number, Q. What is a Negative Number? Ans. Neg...

Q. What is a Negative Number? Ans. Negative numbers  are very important in mathematics. We say that positive and negative numbers are  opposites  of one another. Here

Invariant lines under transformation, What lines are invariant under the tr...

What lines are invariant under the transformation [(103)(01-4)(001)]? I do not know where to even begin to solve this. Please help!!

Using pythagorean theorem to determine z, Two cars begin 500 miles apart.  ...

Two cars begin 500 miles apart.  Car A is into the west of Car B and begin driving to the east (that means towards Car B) at 35 mph & at the similar time Car B begin driving south

Definition of natural exponential function, Definition of Natural exponenti...

Definition of Natural exponential function:   The natural exponential function is f( x ) = e x   where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x

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