7 docs tagged with "integrals"

The two parts of the Fundamental Theorem connecting accumulation functions, derivatives, and definite integrals.

Convergence tests for improper integrals and practical midpoint, trapezoid, and Simpson approximation rules.

The definite integral as accumulated signed area and the indefinite integral as a family of antiderivatives.

A reference for linearity, interval properties, inequalities, and standard antiderivatives of common functions.

A map of antiderivatives, definite integrals, the fundamental theorem, and standard integration techniques.

Worked techniques for integration by parts, trigonometric substitution, and partial-fraction decomposition.

A practical guide to substitution and trigonometric identities for transforming integrals into standard forms.