# Reduction formula (sinx)^n inequality

## Homework Statement part c

## 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??[/B]

Last edited:

Ray Vickson
Science Advisor
Homework Helper
Dearly Missed

## Homework Statement

View attachment 102041
part c

## 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??[/B]

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

Anyway, what does your formula
$$J_{m+2} = m+2 - \frac{1}{m} + 2J_m = m + \frac{1}{m} + 2J_m$$
mean, and where does it come from? Is what you wrote exactly what you meant? Do you need to use parentheses to make your expression clearer?

pasmith
Homework Helper
Use the basic property of integrals that if $f(x) \geq g(x)$ for all $x \in (a,b)$ then $\int_a^b f(x)\,dx \geq \int_a^b g(x)\,dx$.