Integrals

Definition of an IntegralReturn to Top

The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function.

PropertiesReturn to Top

Common IntegralsReturn to Top

Integration by SubstitutionReturn to Top

Integration by PartsReturn to Top

Integration by Trigonometric SubstitutionReturn to Top

Trigonometric identities can be use with integration substitution to simplify integrals. There are three common substitutions.

First Trigonometric SubstitutionReturn to Top

To take advantage of the property

Substitute

After substitution

Second Trigonometric SubstitutionReturn to Top

To take advantage of the property

Substitute

After substitute

Third Trigonometric SubstitutionReturn to Top

To take advantage of the property

Substitute

After substitute