Question

Find the value(s) of c guaranteed by the Mean value Theorem for integrals for the function over the given interval.

f (x) = x^3,       [0, 3]

Answer 1

Step 1:

The function is

is continuous on closed interval , then there exists a number  in the closed interval such that .

Use the fundamental theorem .

Step 2:

Find the value of .

Solution:

.