This is a calculus problem, but the part with which I'm concerned is probably more appropriate in this forum.

Ok, I need to find the area bounded by these two equations:

$\displaystyle y = \cos {x}$

and

$\displaystyle y = 1 - \frac {2x}{\pi}$

First, I need to find the points at which they intersect so I can find the limits of integration. So making them equal to each other, and rearranging:

$\displaystyle \cos x = 1 - \frac {2x}{\pi} \implies \cos x - 1 + \frac {2x}{\pi} = 0$

Now, by looking at the graph, I can tell that the two intersect at $\displaystyle (0, 1), (\frac {\pi}{2}, 0)$ and $\displaystyle (\pi, -1)$. However, can this be solved explicitly? Or do I need to use something like Newton's method to find these values?

Thanks!