For , let be the quarter–circle arc defined by for . If the length of is units, what…

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

Problem

For

k>0

, let

C_k

be the quarter–circle arc defined by

y=\sqrt{k^{2}-x^{2}}

for

0\le x\le k

. If the length of

C_k

\pi

units, what is the value of

k

? (a)

4

(b)

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

(c)

2

(d)

1