Mathematics

Problem

Which of the following definite integrals gives the exact area, in square units, of the region bounded by the graphs of the continuous functions

y=f(x)

and

y=g(x)

on the closed interval

[a,b]

? a)

\displaystyle\int_a^b (f(x)-g(x))\,dx

\displaystyle\left|\int_a^b (f(x)-g(x))\,dx\right|

\displaystyle\int_a^b \lvert f(x)-g(x)\rvert\,dx

\displaystyle\int_a^b (f(x)-g(x))^{2}\,dx