Fundamental Theorem of Calculus

analysis

Definition

Fundamental Theorem of Calculus

Let $f$ be a continuous function on the interval $[a,b]$. Then $F(x)={\int }_a^{b}f(x)dt$ is an antiderivative of $f$. Any antiderivative $F$ of $f$ satisfies:

$${\int }_a^{b}f(x)dx=F(b)-F(a)$$

Instead of writing $F(b)-F(a)$, one can also write $F(x){|}_a^b$ more concisely.