### 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 *x*_{i-1 }< x_{i}^{* }< x_{i}, and*x*_{i} 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 *x*_{i} 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 *x*_{i} 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

*x*_{i} 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*.