Question

AP Calc AB
If, for all real numbers x, f (x) = g (x) + 5, then on any closed interval [a, b] the area of the region between the graphs of f and g is

Answer 1

The area between the graphs of f(x) and g(x) over an interval [a, b] is

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

Since f(x) = g(x) + 5, it follows that |f(x) - g(x)| = |5| = 5, so the value of the integral is always 5 times the length of the integration interval, 5 (b - a).