Answer
$\int_{0}^{\pi/2} x~sin~x~dx \leq \frac{\pi^2}{8}$
Work Step by Step
According to Exercise 27:
$\int_{0}^{\pi/2} x~dx = \frac{(\pi/2)^2-0^2}{2} = \frac{\pi^2}{8}$
On the interval $0 \leq x \leq \frac{\pi}{2}$:
$x~sin~x \leq x$
Therefore, by Property 7:
$\int_{0}^{\pi/2} x~sin~x~dx \leq \int_{0}^{\pi/2} x~dx = \frac{\pi^2}{8}$
$\int_{0}^{\pi/2} x~sin~x~dx \leq \frac{\pi^2}{8}$
