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 n^{th } indexed function in terms of that of n-1^{th }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
sin^{4}x 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 I_{2} in a similar manner, we can write I_{4 }as,
//print line 4
Now, we know that,
//print line5
//print line 6
Here substituting the value of I_{0} in the equation of I_{4 },we have
//print line 7
Thus, by reduction formula the given problem is solved.