Question

How do you find the values of c that satisfy the mean value theorem for integrals?

Answer 1

Solve the equation:

`f(c) = 1/(b-a) int_a^b f(x)dx`

So you need to:

1) find the integral: `int_a^b f(x) dx`,
then
2) divide by `b-a` (the length of the interval)
and, finally
3)set `f(c)` equal to the number found in step 2 and solve the equation.

(There is no guarantee that we can do any of these steps. Just that a solution does exist.)