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

Determine the probability - mean and standard deviation, The scores of stud...

The scores of students taking the ACT college entrance examination are normally distributed with a mean m = 20.1 and a standard deviation s = 5.8. A single student is selected a

Determine matrix of transformation for orthogonal projection, Determine the...

Determine the matrix of transformation for the orthogonal projection onto the line L that passes through the origin and is in the direction Û=(3/13 , 4/13 , 12/13). Determine the r

Evaluate trig functions limits, Evaluate following limits. (a) (...

Evaluate following limits. (a) (b)    Solution There in fact isn't a whole lot to this limit. In this case because there is only a 6 in the denominator we'l

Define regression, Define regression. The main reason of curve fitting ...

Define regression. The main reason of curve fitting is to estimate one of the variables (the dependent variable) from the other (the independent variable). The procedure of est

Ratio, number of consonants to the number of letters in the English Alphabe...

number of consonants to the number of letters in the English Alphabet express answer in ratio

Standard errors of the mean, Standard errors of the mean The series of ...

Standard errors of the mean The series of sample means x¯ 1 , x¯ 2 , x¯ 3 ........ is normally distributed or nearly so as according to the central limit theorem. This can be

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