Question

integrate from 1/2 to 0. arccos x dx

Answer 1

http://www.wolframalpha.com/input/?i=integrate+%28arccosx%29%29

then just plug it F(.5)-F(0)

Answer 2

sorry i dont understand that

Answer 3

\begin{eqnarray*}\int_{1/2}^0 \arccos(x)dx &=& \int_{1/2}^0 (x)'\arccos(x)dx \\ &=& x \arccos(x) \big|_{1/2}^0 + \int_{1/2}^0 \frac{x}{\sqrt{1-x^2}}dx \\
&=& -\frac{\pi}{6} -\sqrt{1-x^2}\big|_{1/2}^0 \\
&=& -\frac{\pi}{6} - 1 + \frac{\sqrt{3}}{2}.\end{eqnarray*}