Find the area of the shaded region between pi/4 and 5pi/4
\[ y=cos(x), y=sin(x) \]
We taking the integral in the desired range for the difference between the 2 functions
\[ \int_{\frac{\pi}{4}}^{\frac{5\pi}{4}} sin(x) - cos(x) \]
\[ = cos(x) + sin(x) \]
Now we need to evaluate:
\[ (cos(\frac{5\pi}{4}) + sin (\frac{5\pi}{4})) - (cos(\frac{\pi}{4}) + sin (\frac{\pi}{4})) \]
\[ (-\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}) - (\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}) \]
\[ = -\frac{4\sqrt{2}}{2} = 2\sqrt{2} \]
So the area between the curve is ~2.8