Real Analysis: Integrals

• October 28th 2008, 09:28 AM
Coda202
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?
• October 28th 2008, 09:39 AM
ThePerfectHacker
Quote:

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