textbook-theory · English
The Fundamental Theorem of Calculus
Section 4.3 from Dan Sloughter's open textbook 'Difference Equations to Differential Equations,' presenting both the Fundamental Theorem of Integral Calculus and the Fundamental Theorem of Differential Calculus with full proofs. The section demonstrates that integration and differentiation are inverse operations, shows how definite integrals may be evaluated using antiderivatives, and proves that every continuous function has an antiderivative constructible via a definite integral with variable upper limit. Worked examples and problem sets covering evaluation of definite integrals, derivatives of integral functions, and area computations are included.
fundamental theorem of calculusintegrationantiderivativesdifferential calculus