Integral inequality with sin proof

  • Thread starter ptolema
  • Start date
1. The problem statement, all variables and given/known data

prove that
integral.jpg
for all x>0

2. Relevant equations

-1 [tex]\leq[/tex] sin t [tex]\leq[/tex] 1

3. The attempt at a solution
the area under the graph is increasing as x increases
also, i tried to write it the sigma way:
leibsigma-1.jpg
then take the limit as n-->infinity
i got stuck trying to figure out how to work with sine in sigma notation, but i'm not even sure if my attempt would get anywhere

can anyone give me any pointers on how to do this?
 
737
0
As x increases, when will the value of the integral be increasing, when will it be decreasing?
 

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