Let denote the arc length of the graph of for

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

Problem

Let

L(k)

denote the arc length of the graph of

y = kx^{2}

for

0 \le x \le 1

, where

k>0

. Which of the following statements about

L(k)

is true? (a)

L(k)

is the same for all positive

k

. (b)

L(k)

is directly proportional to

k

. (c)

L(k)

increases as

k

increases. (d)

L(k)

increases for

0<k<1

and decreases for

k>1