Fundamental Theorem of Calculus
If and is Riemann integrable, then .
Theorem 2.4 (Fundamental Theorem of Calculus)
Let for some Riemann integrable function Then
Proof
For ,
The integral over this interval is by the mean-value theorem and Taylor’s theorem. The limit is therefore .
Related
Stated in
- Theorem 2.4 (Fundamental Theorem of Calculus)§2.2 Fundamental Theorem of Calculus (FTC)