# Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of y=sin(x) and y=cos(x), how do you find the area of R?

$\sqrt{2} - 1$
$R = {\int}_{0}^{\frac{\pi}{4}} \left(\cos \left(x\right) - \sin \left(x\right)\right) \mathrm{dx} = \left(\sin \left(\frac{\pi}{4}\right) + \cos \left(\frac{\pi}{4}\right)\right) - \left(\sin \left(0\right) + \cos \left(0\right)\right) = 2 \frac{\sqrt{2}}{2} - 1 = \sqrt{2} - 1$