The Theorems of Integral Calculus
Below are statements of theorems from integral calculus with accompanying visualizations.
The Fundamental Theorem of Calculus
If is continuous on , then:
- If , then . Another way of saying this is .
- , where is any antiderivative of (that is, ).
The Mean Value Theorem for Integrals
If is continuous on , then there is a number in such that .