Q:

How to find the original function from a definite integral and its value

What are the steps to solving this problem? (Thank you in advance)
The average value of a continuous function f (x) on the closed interval [3,7] is 18.
What is the value of (integral)[3,7] f (x)dx ?

A:

The average value of a function $f(x)$ over an interval $[a,b]$ is defined as $$\frac{\int \limits_{a}^{b} f(x) \mathrm d x}{b-a}.$$
Using this definition we have $\int \limits_{3}^{7} f(x) \mathrm d x = 18 \times 4 = 72.$

