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:
Solve Integration of
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 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.