Mathematics

Problem

Suppose

f

and

g

are continuous on

[a,b]

and satisfy

f(x)\ge g(x)

for every

x

in that interval, with

f(x)>g(x)

for at least one value of

x

. Determine whether

\displaystyle\int_{a}^{b}\bigl(f(x)-g(x)\bigr)\,dx

is positive, negative, or zero, and briefly justify your conclusion.