# Definite Integrals

# Calculus Terms

## Get down with the lingo

### 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}, and 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*for

_{i}*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*for

_{i}*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*for

_{i}*i*= 1,…,

*n*divides the interval [

*a*,

*b*] into

*n*subintervals.

### Trapezoid Sum:

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:

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:

The 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*.

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