Reduction formula (sinx)^n inequality

  • #1
58
1

Homework Statement


problem 4.PNG

part c

Homework Equations



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]
 
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  • #2
kenok1216 said:

Homework Statement


View attachment 102041
part c

Homework Equations



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
[tex]J_{m+2} = m+2 - \frac{1}{m} + 2J_m = m + \frac{1}{m} + 2J_m [/tex]
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?
 
  • #3
Use the basic property of integrals that if [itex]f(x) \geq g(x)[/itex] for all [itex]x \in (a,b)[/itex] then [itex]\int_a^b f(x)\,dx \geq \int_a^b g(x)\,dx[/itex].
 

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