Could someone please help me evaluate this integral? The integral is
$$
\int_{0}^{1/\sqrt{\vphantom{\large A}2\,}}
{\arccos\left(x\right) \over \sqrt{\vphantom{\large A}1 -x^2\,}\,}\;{\rm d}x 
$$
I was just wondering if I could use substitution to solve this problem or if I had to solve it a different way.

$$
\int \Big(\arccos x\Big) \left( \frac{dx}{\sqrt{1-x^2}} \right) = \int \Big( u \Big) \Big(-du\Big)
$$
(If you don't know what the derivative of the arccosine function is, then that's what you need to look up.)
When $x=0$ then $u=\pi/2$ and when $x=1/\sqrt{2}$ then $u=\pi/4$ (you need to recall some trigonometry to see where those numbers come from).  So
$$\int_{\pi/2}^{\pi/4}\cdots\cdots\, (- du) = \int_{\pi/4}^{\pi/2} \cdots\cdots\, du$$
i.e. interchanging $\pi/2$ and $\pi/4$ is canceled out by dropping the minus sign.
