The discussion revolves around the definite integral of the function sin²(nx)/sin²(x) from 0 to π. Participants explore methods for solving this integral, particularly focusing on the use of mathematical induction and questioning its appropriateness in this context.
Participants do not appear to reach a consensus on the appropriateness of using mathematical induction for this integral, and there are competing views on the validity of the method and the results derived from it.
There are indications of confusion regarding the application of mathematical induction, and participants express uncertainty about the correctness of the method used to solve the integral.
How do you use induction here? You haven't even given us a result!anirudhsharma1 said:pi
∫sin^2(nx)/sin^2(x) dx
0
I tried using mathematical induction and did arrive at the correct result but was wondering if a better method could be used to solve it?
Are you confused about what induction means?anirudhsharma1 said:putting n=1,n=2
we get pi, and pi as the result
so i generalised it for 'n'.
thats the reason i asked for the solution because this is definitely an improper method.