Integrals

Concepts

• Definite integral 10 exercisesThe definite integral of f on [a,b] is the limit of the Riemann sums as n→∞. It represents the signed net area between the graph…
• Riemann sums 10 exercisesA Riemann sum approximates the area under a curve by dividing [a,b] into n rectangles of width Delta x and adding their areas, wi…
• Fundamental theorem of calculus 20 exercisesIt links derivatives and integrals: a definite integral equals an antiderivative evaluated at the endpoints, and differentiating…
• Antiderivative 10 exercisesAn antiderivative of f is a function F such that F^prime=f. If F is an antiderivative of f, all the others on an interval differ…
• Indefinite integral 11 exercisesThe indefinite integral of f is the family of all its antiderivatives, written with a constant of integration C.
• Integration by substitution 10 exercisesTechnique that simplifies an integral through the change of variable u=g(x), du=g^prime(x) dx.
• Integration by parts 10 exercisesIntegration by parts is a technique for integrating products of functions, derived from the product rule. It transforms ∫ u dv in…
• Area between curves 10 exercisesThe area between the graphs of f and g on [a,b], with f≥ g, is the integral of the difference f-g. If the curves cross, the inter…