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Average Value of a Function definitions

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  • Definite Integral
    Represents the total area under a curve between two points, capturing accumulated change over an interval.
  • Average Value
    Describes the mean output of a function across an interval, calculated using integration and interval length.
  • Interval
    A continuous set of x-values, typically denoted by two endpoints, over which a function is analyzed.
  • Riemann Sum
    An approximation method using sums of areas of rectangles to estimate the area under a curve.
  • Subinterval
    A smaller segment within a larger interval, used to partition the domain for summation or integration.
  • Limit
    A concept describing the value a sequence or function approaches as the input or index grows without bound.
  • Delta x
    Represents the width of each subinterval in a partition, calculated as the total interval length divided by the number of subintervals.
  • Antiderivative
    A function whose derivative yields the original function, used to compute definite integrals.
  • Fundamental Theorem of Calculus
    Connects differentiation and integration, allowing evaluation of definite integrals using antiderivatives.
  • Bound
    An endpoint of an interval, serving as a limit for integration or summation.
  • Summation
    The process of adding a sequence of terms, often used to approximate integrals before taking limits.
  • Output
    The value produced by a function for a given input, representing the function's response.
  • Input
    A value substituted into a function, typically represented by x, determining the corresponding output.
  • Rectangle
    A geometric shape used in Riemann sums to approximate areas under curves, defined by height and width.
  • Equation
    A mathematical statement expressing the relationship between quantities, such as the formula for average value.