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Definite Integrals 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 xi-1 < xi* < xi, and xi, 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 xi for i = 1,…,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,…,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:

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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