User:Spewin

Given the a polynomial

$$f(x) = \Sigma_{i=0}^n p_i x^k$$

The definite integral of f(x) is

$$\int_a^b f(x) dx = \Sigma_{i=0}^n p_k \frac{b^{k+1} - a^{k+1}}{k+1}$$

how do I factor out a (b-a) term so that I can find f(c) where for a < c < b, $$\int_a^b f(x) dx = F(b) - F(a) = f(c)(b-a)? $$