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- Dartmouth College - Department of Mathematics - The Fundamental Theorem of Calculus
- Campus Manitoba PressbooksEDU Network - Calculus: Volume 2 (Second University of Manitoba Edition) - The Fundamental Theorem of Calculus
- Story of Mathematics - Fundamental Theorem of Calculus - Parts, Application, and Examples
- California State University Northridge - Fundamental Theorem of Calculus (PDF)
- Khan Academy - Proof of fundamental theorem of calculus
- Purdue University Northwest - The Fundamental Theorem of Calculus (PDF)
- University of Notre Dame - The Fundamental Theorem of Calculus
- Open Library Publishing Platform - Introduction to Mathematical Analysis for Business - Fundamental Theorem of Calculus
- Mathematics LibreTexts - The Fundamental Theorem of Calculus
- Clark University - Proof of the Fundamental Theorem of Calculus
- Whitman College - Mathematics - The Fundamental Theorem of Calculus
- The Pennsylvania State University - Open Resource Publishing - Fundamental Theorem of Calculus
- OpenStax - Calculus Volume 1 - The Fundamental Theorem of Calculus
- Auburn University - Fundamental theorem of calculus
- Mathematical Association of America - Teaching the Fundamental Theorem of Calculus: A Historical Reflection - Integration from Cavalieri to Darboux
fundamental theorem of calculus
fundamental theorem of calculus, Basic principle ofcalculus. It relates thederivative to theintegral and provides the principal method for evaluating definiteintegrals (seedifferential calculus;integral calculus). In brief, it states that anyfunction that is continuous (seecontinuity) over an interval has an antiderivative (a function whose rate of change, or derivative, equals the function) on that interval. Further, the definiteintegral of such a function over an intervala <x <b is the differenceF(b) −F(a), whereF is an antiderivative of the function. This particularly eleganttheorem shows theinverse function relationship of the derivative and the integral and serves as the backbone of the physical sciences. It wasarticulated independently byIsaac Newton andGottfried Wilhelm Leibniz.