Question

If the function f' has a continuous derivative on [0, c] then integral from 0 to c f"(x)dx=​

Answer 1

The result follows from the fundamental theorem of calculus. Since $f''(x)$ is the derivative of $f'(x)$, we have

$\displaystyle \int_0^c f''(x) \, dx = \boxed{f'(c) - f'(0)}$

(E)