textbook-theory · English
Difference Equations to Differential Equations — Section 4.4: Using the Fundamental Theorem
Section 4.4 of Dan Sloughter's open calculus textbook 'Difference Equations to Differential Equations' presents the use of the Fundamental Theorem of Integral Calculus to evaluate definite integrals by finding antiderivatives. The section introduces indefinite integrals (general antiderivatives), standard integration formulas for polynomial and trigonometric functions, linearity properties, and the technique of integration by substitution (reversing the chain rule). Worked examples cover polynomial, trigonometric, and composite-function integrands for both indefinite and definite integrals, followed by a comprehensive problem set.
indefinite integralsintegration by substitutionFundamental Theorem of Calculusantiderivatives