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Math Help - Real Analysis: Integrals

  1. #1
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    Real Analysis: Integrals

    Without evaluating the integral, how does one show that:
    0 less than or equal to the integral from 0 to pi/6 sin(x) dx greater than or equal to pi/12?
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  2. #2
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    Quote Originally Posted by Coda202 View Post
    Without evaluating the integral, how does one show that:
    0 less than or equal to the integral from 0 to pi/6 sin(x) dx greater than or equal to pi/12?
    For x\in [0,\pi/6] we have 0\leq \sin x\leq \tfrac{1}{2}.
    Thus, 0\leq \int_0^{\pi/6} \sin x dx\leq \int_0^{\pi/6}\frac{dx}{2} = \frac{\pi}{12}
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