Reduction formula (sinx)^n inequality

1. Jun 14, 2016

kenok1216

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

part c

2. Relevant equations

3. The attempt at a solution
Jm+2=m+2-1/m+2 Jm=m+1/m+2 Jm
hence Jm+2<Jm
should i expend Jm+2 Jm+1 Jm to the term J0 then compare them???
why the inequality is <= but not <?
should i use M.I to proof it??

Last edited: Jun 14, 2016
2. Jun 14, 2016

Ray Vickson

Please stop using a bold font; it looks like you are yelling at us.

$$J_{m+2} = m+2 - \frac{1}{m} + 2J_m = m + \frac{1}{m} + 2J_m$$
Use the basic property of integrals that if $f(x) \geq g(x)$ for all $x \in (a,b)$ then $\int_a^b f(x)\,dx \geq \int_a^b g(x)\,dx$.