Mathematics

Problem

Let

f

and

g

be continuous function on

a \le x \le b

and set

p(x) = \max\{f(x), g(x)\}

and

q(x) = \min\{f(x), g(x)\}

, then the area bounded by the curves

y = p(x)

y = q(x)

and the ordinates

x = a

and

x = b

is given by a.

\int_a^b |f(x) - g(x)| dx

\int_a^b |p(x) - q(x)| dx

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

\int_a^b \{p(x) - q(x)\} dx