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 Sums.
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.