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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Originally Posted by Coda202 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 $\displaystyle x\in [0,\pi/6]$ we have $\displaystyle 0\leq \sin x\leq \tfrac{1}{2}$. Thus, $\displaystyle 0\leq \int_0^{\pi/6} \sin x dx\leq \int_0^{\pi/6}\frac{dx}{2} = \frac{\pi}{12}$
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