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

Example of circle graphs, Q. Example of circle graphs? Ans. The Un...

Q. Example of circle graphs? Ans. The United States Government pays obligations annually, called "outlays". Medicare contributes to the health and well being of aged an

Division, Before taking up division of polynomials, let us acquaint...

Before taking up division of polynomials, let us acquaint ourselves with some basics. Suppose we are asked to divide 16 by 2. We know that on dividing 16 by

Shortricks, shortricks of compound interest

shortricks of compound interest

Circumference of a circle, How far will a bowling ball goes in one rotation...

How far will a bowling ball goes in one rotation if the ball has a diameter of 10 inches? (π = 3.14) 1. 78.5 in 2. 31.4 in 3. 62.8 in 4. 15.7 in 2. The circumfere

The number of filtering steps, The amount of particulate matter left in sol...

The amount of particulate matter left in solution during a filtering process is given by the equation p(n) = 500(2) -0.8n , where n is the number of filtering steps. Find the amoun

Laws of indicies in fraction.., help to solve the laws of indicies chapter ...

help to solve the laws of indicies chapter 9c book 3 high school example19to the power3_2 what is answer

Constructing tables versus rote learning maths, CONSTRUCTING TABLES VERSUS ...

CONSTRUCTING TABLES VERSUS ROTE LEARNING :  Ask any adult how she would help a child to acquire simple multiplication facts. There is a very strong possibility that she would say,

Determine the area of the matting, A circular print is being matted in a sq...

A circular print is being matted in a square frame. If the frame is 18 in by 18 in, and the radius of the print is 7 in, what is the area of the matting? (π = 3.14) a. 477.86 in

Find out that the relation is an equivalent relation or not, Let m be a pos...

Let m be a positive integer with m>1. Find out whether or not the subsequent relation is an equivalent relation. R = {(a,b)|a ≡ b (mod m)} Ans: Relation R is illust

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