# Indefinite Integrals Terms

## Get down with the lingo

### Partial Fraction Decomposition

Reducing the degree of the numerator or the denominator of a rational function.

### Integration By Parts

A technique for performing integration where .

### Improper Integrals

An definite integral  is called an improper integral when the limits of integration are infinite (a = -∞, b = ∞) or the function becomes unbounded in [a, b].

### Reimann Sum

The Reimann Sum of a function f(x) over an interval [a, b] is defined as  where xi-1 < xi< xi, and xi for i = 1,…,n divides the interval [a, b] into n subintervals.

### Left-Hand Sum

The Left-Hand Sum of a function f(x) over an interval [a, b] is defined as  where xi for i = 1,…,n divides the interval [a, b] into n subintervals.

### Right-Hand Sum

The Right-Hand Sum of a function f (x) over an interval [a, b] is defined as where xi for i = 1,…,n divides the interval [a, b] into n subintervals.

### Midpoint Sum

The Midpoint Sum of a function f (x) over an interval [a, b] is defined as where , and xi for i = 1,…,n divides the interval [a, b] into n subintervals.

### Trapezoid Sum

The trapezoid sum is the average between the Left-Hand and Right-Hand Sum.

### Average Value Of A Function

The average value of a continuous function f on the closed interval [a, b] is defined as .

### Concavity

The concavity of a function describes whether the function is curving up, down or not curving at all.

### Critical Point

The derivative of the function at the critical point is 0.

### Inflection Point

The point (x-value) where the function changes concavity.

### Secant Line

A line joining two points on the graph of a function.

### Tangent Line

A line that touches the graph of a function f (x) at a point.

### Differentiability

If the limit exists, the function f (x) is differentiable at x = a.