The line and the parabola

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

Problem

The line

y=ax

and the parabola

y=x^{2}

, together with the

y

-axis, enclose a region of area

8

square units. The positive value of

a

is (a)

2\sqrt[3]{3}

(b)

\sqrt[3]{12}

(c)

2\sqrt[3]{6}

(d)

3\sqrt[3]{2}