Math problem where graphing calculator may slow you down - part II.

[Thomas Klemm]

(09-13-2014 09:12 PM)Bunuel66 Wrote:  Integrating is straightforward and gives 4/sqrt(2) over 0 to 2pi

We should make sure that the integral is always < 4. Thus we calculate it up to the first zero of the function \(f(x)\) which occurs at \(x=\pi\):
\[
\int_{0}^{\pi}\max(\sin(x),\cos(x))dx=1+\sqrt{2}\approx 2.41421
\]

Cheers
Thomas