Integrals

An antiderivative is a differentiable function $F$ whose derivative is equal to $f$ (i.e., $F' = f$).

Defined integrals are used in many practical situations that require distance, area, and volume calculations.

A definite integral is the area of the region in the $xy$-plane bound by the graph of $f$, the $x$-axis, and the vertical lines $x=a$ and $x=b$.

The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function to the concept of the integral.

An indefinite integral is defined as $\int f(x)dx = F(x)+ C$, where $F$ satisfies $F'(x) = f(x)$ and where $C$ is any constant.

Integration by substitution is an important tool for mathematicians used to find integrals and antiderivatives.

A transcendental function is a function that is not algebraic.

Numerical integration is a method of approximating the value of a definite integral.