For , let be the region bounded by the curves and from to . If the area of is , what…

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

Problem

For

k>0

, let

S

be the region bounded by the curves

x = ky

and

x = y^{2}

from

y=0

y=k

. If the area of

S

6

, what is the value of

k

? (a)

\sqrt[3]{18}

(b)

\sqrt[3]{12}

(c)

\sqrt[3]{36}

(d)

\sqrt[3]{6}