Fundamental Theorem of Calculus

If f is continuous in [a,b], the function F defined in [a,b] as:

is derivable in (a,b) and F’(x) = f(x)

NOTE: f derivable→f continuous→f integrable

True-False Question

Decide if the following sentences are true or false:

a) All the continuous functions are integrable functions

True. False.

b) All the derivable functions are integrable functions

True. False.

c) Some integrable functions are derivable functions

True. False.

d) All the integrable functions are continuous functions

True. False.