# Accuracy of Fundamental thereom compared to MVT

1. Mar 7, 2010

### nobahar

Hello!
The Mean Value thereom gives F(b)-F(a) = f(c).(b-a) Where f is F' and c is the value of x at which it's derivate is equal to the average rate of change over the interval a to b for F.
The Fundamental thereom of calculus also gives F(b)-F(a) = $$(\frac{1}{b-a} \left \left \int _{a}^{b}f(x)dx)(b-a)$$
Why is the second more accurate than the first, surely both give the average rate of change multiplied by the same interval, (b-a)? Is it to do with practical applications, and determining the f(c) value?
Any pointers/help much appreciated.