Consider two parametric curves on with a common -coordinate given by

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

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}

(b)

\dfrac{1}{2}

(c)

\sqrt{2}-1

(d)

1-\sqrt{2}