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Integral question

  • Thread starter Buri
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  • #1
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Homework Statement



Prove that [tex]\int_{0}^{x}\frac{\sin(t)}{t+1}dt > 0[/tex]

Homework Equations



It asks me to do this without actually calculating it and I can't use the Fundamental Theorem of Calculus.

The Attempt at a Solution



Okay, I see why this should be true as the function oscillates (with smaller bumps over time) around the x-axis so only the first bump really counts. I've tried considering small intervals where I know the function has certain values, but I can't seem to get anywhere with that idea either. Any help?
 
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Answers and Replies

  • #2
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Even a hint would be greatly appreciated! Thanks!
 
  • #3
273
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Ughhh I figured it out! I just showed that the integral from [0,pi] is larger in absolute value than the integral from [pi,2pi]. Continuing in this fashion (i.e. pairing up consecutive intervals) proves the assertion.
 

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