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Reduction formula (sinx)^n inequality

  1. Jun 14, 2016 #1
    1. The problem statement, all variables and given/known data
    problem 4.PNG
    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. jcsd
  3. Jun 14, 2016 #2

    Ray Vickson

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    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?
     
  4. Jun 14, 2016 #3

    pasmith

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    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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