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# Calculus Terms

## Get down with the lingo

### Fundamental Theorem Of Calculus

This theorem provides a relation between the derivative and the definite integral of a function.

### Second Fundamental Theorem Of Calculus

This theorem provides a method of differentiating an integral.

### Integration By Parts

A technique for performing integration where .

### Improper Integral

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, andxi 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

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

### Concavity

This 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.