For the curves and on the interval

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

Problem

For the curves

x = y^{3}

and

x = y^{2}

on the interval

0 \le y \le 1

, which statement correctly identifies the curve that forms the right-hand boundary of the region between the two graphs? (a)

x = y^{3}

is to the right of

x = y^{2}

for all

y

[0,1]

. (b) The curves switch roles at

y = \dfrac23

;

x = y^{2}

is to the right when

y < \dfrac23

and

x = y^{3}

is to the right when

y > \dfrac23

. (c)

x = y^{2}

is to the right of

x = y^{3}

for all

y

[0,1]

. (d) The curves switch roles at

y = \tfrac12

;

x = y^{3}

is to the right when

y < \tfrac12

and

x = y^{2}

is to the right when

y > \tfrac12