Mathematics

Problem

For curves

y=f(x)

and

y=g(x)

with

f(x)\ge g(x)

on the interval

[a,b]

, which of the following integrals gives the area enclosed between the two curves from

x=a

x=b

? a)

\displaystyle \int_a^b \bigl[f(x)+g(x)\bigr]\,dx

\displaystyle \frac12\int_a^b \bigl[f(x)-g(x)\bigr]\,dx

\displaystyle \int_a^b \bigl[f(x)-g(x)\bigr]\,dx

\displaystyle \int_a^b \bigl[g(x)-f(x)\bigr]\,dx