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

Mean value theorem function, Mean Value Theorem : Suppose f (x) is a funct...

Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on

Right angled triangle, In proving relation of trigonometric ratios we becam...

In proving relation of trigonometric ratios we became confused that what should we do next, so to complete any question quickly what should we do?

Estimation of difference among two means-illustration, A comparison of the ...

A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and

SAT question, In a certain class, one half of the male students and two thi...

In a certain class, one half of the male students and two thirds of the female students speak French. If there are three fourths as many girls as boys in the class. What fraction o

Shares and dividend, i need some information on this topic for my holidays ...

i need some information on this topic for my holidays project..plz guide me what to do

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

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