Integral Calculus Concepts

Vocabulary flashcards covering key concepts in integral calculus.

Definite Integral

The integral of a function over a specified interval [a, b].

Riemann Sum

A method for approximating the definite integral by dividing the interval into smaller subintervals and summing the areas of rectangles.

Integration by Parts

A technique used to integrate products of functions, based on the product rule of differentiation.

Limit of a Riemann Sum

The value that a Riemann sum approaches as the width of the subdivisions approaches zero.

Dirichlet Function

A function defined as 1 for rational numbers and 0 for irrational numbers; it is not integrable.

Properties of Definite Integrals

Rules that apply to definite integrals, such as the integral of a constant and the additive property.

Cauchy Condition

A criterion for the convergence of a series, stating that if a series is convergent, its sequence of partial sums is Cauchy.

Newton-Leibniz Theorem

A fundamental theorem relating differentiation and integration, stating that the definite integral of a function can be computed using its antiderivative.

Substitution Method

A technique for evaluating integrals by changing the variable of integration.

Estimating Errors in Integration

Techniques used to assess the accuracy of numerical integration methods.