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Riemann Sums definitions

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  • Sigma Notation
    A compact symbolic method for expressing the sum of many terms, using an index to indicate the range and a formula for each term.
  • Index of Summation
    A variable, often a letter, that indicates the starting and ending values for a sum in sigma notation.
  • Finite Sum
    A total obtained by adding a specific, limited number of terms, often represented using sigma notation.
  • Sum and Difference Rule
    A property allowing the separation of a sum or difference inside a summation into individual summations for easier calculation.
  • Constant Multiple Rule
    A property that permits a constant factor to be moved outside the summation, simplifying the computation.
  • Riemann Sum
    An approximation of the area under a curve by summing the areas of rectangles determined by function values at specific points.
  • Subinterval
    A segment of the total interval over which a function is approximated, corresponding to one rectangle in a Riemann sum.
  • Delta x
    The uniform width of each subinterval or rectangle, calculated as the total interval length divided by the number of rectangles.
  • Left Endpoint Approximation
    A Riemann sum method using the leftmost value of each subinterval to determine the height of each rectangle.
  • Right Endpoint Approximation
    A Riemann sum method using the rightmost value of each subinterval to determine the height of each rectangle.
  • Midpoint Approximation
    A Riemann sum method using the average of the left and right endpoints of each subinterval to set the rectangle's height.
  • Subinterval Width Formula
    An expression, (b-a)/n, that determines the width of each rectangle in a Riemann sum based on the interval and number of rectangles.
  • Function Value
    The output of a function at a specific input, used as the height of rectangles in Riemann sums.
  • Rectangle Area
    The product of a rectangle's height and width, representing a portion of the area under a curve in Riemann sums.
  • Summation Notation
    A mathematical shorthand using the Greek letter Sigma to represent the addition of a sequence of terms.