Does integrating on both the sides of inequality with the same upper and lower limits with respect to same variable somehow affect the inequality. I saw an example lets say, Sin x < x ,x>0 Integrating repeatedly and along with some addition changes,makes the inequality to a Taylor series transform. Thus making the inequality an equality if we integrate infinite times w.r.t. X .

  • $\begingroup$ see the ineqaulity subsection here: en.wikipedia.org/wiki/Integral#Inequalities (I don't know how to directly link to it) $\endgroup$
    – Shreya
    Jun 13, 2016 at 18:32
  • $\begingroup$ If $f(x)\le g(x)$ for $x\in [a,b]$, then $\int_a^b f(x)\,dx \le \int_a^b g(x)\,dx$ $\endgroup$
    – Mark Viola
    Jun 13, 2016 at 18:42
  • $\begingroup$ If I repeatedly integrate till infinite times then it may change to equality as in the case I had put in the question $\endgroup$ Jun 13, 2016 at 18:46


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