Consider the functions and

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

Problem

Consider the functions

f(x)=\lvert x\rvert

and

g(x)=x^{2}-1

. The graphs of

f

and

g

enclose a bounded region in the plane. What is the exact area of this region? (a)

\dfrac{\sqrt5-1}{3}

(b)

\dfrac{11+5\sqrt5}{6}

(c)

\dfrac{7+5\sqrt5}{6}

(d)

\dfrac{7+5\sqrt5}{12}