In how many different ways can you find answers to the following integrals?

\(\displaystyle {\int_{0}^{\pi} \cos 2x \, dx}\)

\(\displaystyle {\int_{0}}^{\frac{\pi}{2}} \sin^2 x \, dx\)

\(\displaystyle {\int_{-1}^{1}} \arcsin x \, dx\)

\(\displaystyle {\int_{-1}^{1}} \arccos x \, dx\)

It might be useful to sketch the graphs of the functions to be integrated. You may wish to use graphing software such as Desmos or GeoGebra.

Do the functions have any symmetry that can help?

Are there any trigonometric identities you know that involve these functions?