9. Fundamental Theorem of Calculus

Fundamental Theorem of Calculus

Fundamental theorem of calculus contains two important theorems namely:

First fundamental theorem of integral calculus

Let f be a continuous function on the closed interval [a, b] and let A (x) be the area function. Then A′(x) = f (x), for all x ∈ [a, b].

Second fundamental theorem of integral calculus

Let f be a continuous function defined on the closed interval [a, b] and F be an antiderivative of f.

Then ∫_a^b f(x) dx= [F(x)]_a^b = F(b) – F(a)