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 inverse matrix, Determine the inverse of the following matrix, i...

Determine the inverse of the following matrix, if it exists. We first form the new matrix through tacking onto the 3 x 3 identity matrix to this matrix.  It is, We

Areas of a rectangle, a rectangular field with a path around it measures 1...

a rectangular field with a path around it measures 120m by 50m.if the path is 1m wide all around,(a)find the length of the outer edge of the path.(b)find the area of the path

Interquarticles, (i may have spelled it wrong)but i forgot how to do them.

(i may have spelled it wrong)but i forgot how to do them.

Horizontal asymptotes, Horizontal asymptotes : Such as we can have vert...

Horizontal asymptotes : Such as we can have vertical asymptotes defined in terms of limits we can also have horizontal asymptotes explained in terms of limits. Definition

Chi-square hypothesis tests as non-parametric test(x2), Chi-square hypothes...

Chi-square hypothesis tests as Non-parametric test(X2) They contain amongst others i.    Test for goodness of fit ii.   Test for independence of attributes iii.  Test

Project, report on shares and dovidend using newspaper

report on shares and dovidend using newspaper

5th grade, 6 and 3/8 minus 1 and 3/4

6 and 3/8 minus 1 and 3/4

Inverse functions, We have seen that if y is a function of x, then fo...

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f

Calculate the investment - apr 4 percent, Suppose you start saving today fo...

Suppose you start saving today for a $55,000 down payment that you plan to make on a house in 7 years,  assume that you make no deposits into the account after the initial deposit,

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