It might be difficult for you to read this integral in non latex form, but i'll try my best.(adsbygoogle = window.adsbygoogle || []).push({});

As i dont know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I.

1. The problem statement, all variables and given/known data

I(n)=∫ (sinx)^n dx [with limits of the integral as : from zero (0) to ∏/2 (pi/2)

Using the above equation, it is required to prove that :

I(n+2)= I(n) * (n+1)/(n+2) [again , I(n) means I subscript n ie nth term of a sequence]

2. Relevant equations

the formula for integration by parts

3. The attempt at a solution

I have tried to integrate it by parts using various ways but all of them failed to prove the required result.

One of them was :

∫ [sin^-2(x)*(sin(x))^(n+2)] dx [with the same limits ofcourse]

even after subsituting 1-cos^2(x) for sin^2(x) the problem could not be solved,

please help me solve it.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need help in deriving this reduction formula

**Physics Forums | Science Articles, Homework Help, Discussion**