Reduction formulae, Mathematics


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.


Posted Date: 7/23/2012 5:03:50 AM | Location : United States

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