Area, Volume, and Arc Length
Calculus Terms
Get down with the lingo
Area Under The Curve
The area of the region bounded by the graph of function f(x) and the x-axis for a ≤ x ≤ b, is given by the definite integral
.Polar Coordinates
Polar coordinates use a two-dimensional coordinate system where each point is represented by a distance and angle from a fixed point.Volumes Of Solids Of Revolution
The volume of the solid figure obtained by rotating a curve around a straight line.Disk Method
This is a method for finding the volumes of solids of revolution when the cross sections are taken perpendicular to the axis of revolution and the axis is the boundary of the plane region.Washer Method
This is a method for finding the volumes of solids of revolution when the cross sections are taken perpendicular to the axis of revolution and the axis is not the boundary of the plane region.Arc Length
The arc-length of a continuous function f(x) on a closed interval [a,b] is defined as
.Parametric Equations
The equations in which rather than the coordinates x and y being defined in terms of each other, they are defined in terms of another parameter t.Improper Integral
A 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 
, andxi 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
The concavity of a function describes whether the function is curving up, down or not curving at all.