The function is continuous and .

Mean value theorem for integrals:  

If is continuous on , then there exist a number in such that

.

Since the function is continuous on , so by the mean value theorem, there exist a number in .

such that

.

We have, .

Substitue in .

.

From the above expression it is observed that there exist a number in

such that .

Therefore, the function value takes on the value on .

The function value takes on the value atleast once on .