Fundamental theorem of calculus
Integration and differentiation undo each other: a definite integral is the change in any antiderivative. History: 1660s to 1680s.
How to work it out
- 1
The statement:
- 2
Integration and differentiation undo each other: a definite integral is the change in any antiderivative.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ \int_a^b f(x)\,dx = F(b) - F(a) \]
Riemann sums of xĀ² on [0, 1] approaching F(1) ā F(0) = 1/3 (computed)
| Rectangles | Sum | Sum ā 1/3 |
|---|---|---|
| 4 | 0.468750 | 1.35e-1 |
| 10 | 0.385000 | 5.17e-2 |
| 100 | 0.338350 | 5.02e-3 |
| 1000 | 0.333834 | 5.00e-4 |
| 100000 | 0.333338 | 5.00e-6 |
Questions
What is the fundamental theorem of calculus?
Integration and differentiation undo each other: a definite integral is the change in any antiderivative.
Who is the Fundamental theorem of calculus associated with?
Isaac Newton, Gottfried Wilhelm Leibniz.