Mathematics

Problem

Which of the following statements correctly gives the area enclosed between the graph of a continuous function

y=f(x)

and the

x

-axis on

[a,b]

when

f(x)

takes both positive and negative values in the interval? a)

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

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

\displaystyle \int_a^b |f(x)|\,dx

\displaystyle \int_{f(x)\ge 0} f(x)\,dx