Find the region bounded by $y=x \sin x$, and $y=x$

Question

Find the area bounded by the region $y=x \sin(x)$, and $y=x$, for $0\le x\le \frac{\pi}{2}$.

My attempt

Area $=\int_\limits{0}^{\frac{\pi}{2}}(x-x\sin(x))dx$

After integrating I got:

$$[\frac{x^2}{2}+x\cos(x)-\sin(x)]_0^\frac{\pi}{2}$$

Is my answer right?

Which leads me to get approximately .2337 units squared.

Answer 1

Your answer is correct to four decimal places (see e.g. WolframAlpha for confirmation), just make sure you can also get the correct exact answer (in terms of $\pi$).