Reduction formula (sinx)^n inequality

[kenok1216]

Homework Statement

part c

Homework Equations

The Attempt at a Solution

J_m+2=m+2-1/m+2 J_m=m+1/m+2 J_m
hence J_m+2<J_m
should i expend J_m+2 J_m+1 J_m to the term J₀ then compare them?
why the inequality is <= but not <?
should i use M.I to proof it??[/B]

 

[Ray Vickson]

Homework Statement

View attachment 102041
part c

Homework Equations

The Attempt at a Solution

J_m+2=m+2-1/m+2 J_m=m+1/m+2 J_m
hence J_m+2<J_m
should i expend J_m+2 J_m+1 J_m 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]

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