Integrating arccos x
To evaluate
\[\int^1_0 cos^{-1} xdx\]
consider the following graph.
The area under the curve of
\[y=cosx\]
is adjacent to both
\[x\]
and
\[y\]
axes so
\[\int^1_0 cos^{-1} y dy= \int^{\pi /2}_0 cosx dx= [sinx]^{\pi /2}_0 =1\]
.
