Mathematics

Problem

Consider two parametric curves on

0\le t\le \dfrac{\pi}{4}

with a common

x

-coordinate given by

x(t)=t

. The first curve has

y_{1}(t)=\cos t

and the second has

y_{2}(t)=\sin t

. What is the exact area between the two curves over this interval? a)

\dfrac{\sqrt{2}}{2}

\dfrac{1}{2}

\sqrt{2}-1

1-\sqrt{2}