Consider the two curves and on the interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the two curves

y = x

and

y = x^{3}

on the interval

-1 \le x \le 2

. (i) Determine all points of intersection of the two curves that lie in the interval

[-1,2]

. (ii) Hence set up the appropriate definite integral(s) and calculate the total area of the region enclosed between the two curves from

x = -1

x = 2

. Express your answer in exact form.