BackIntroduction to Definite Integrals definitions
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1/15BackSkip to main contentBackDefinite Integral
True area under a curve between two bounds, found by taking the limit of Riemann sums as the number of rectangles approaches infinity. Riemann Sum
Approximation of area under a curve using a finite number of rectangles, improved as more rectangles are used. Bound
Specific values on the x-axis that mark the start and end points for calculating area under a curve. Lower Bound
Starting value on the x-axis for integration, indicating where area calculation begins. Upper Bound
Ending value on the x-axis for integration, indicating where area calculation stops. Indefinite Integral
Expression representing a family of functions without specific bounds, lacking a true area interpretation. Summation
Notation used to add up areas of rectangles in Riemann sums, often involving a limit as the number increases. Sum and Difference Rule
Property allowing the integral of a sum or difference to be split into separate integrals with unchanged bounds. Constant Multiple Rule
Property allowing a constant factor in a function to be moved outside the integral without affecting the bounds. Order of Integration Rule
Property stating that switching the bounds of integration reverses the sign of the integral's result. Zero Width Interval Rule
Property stating that integrating over an interval with identical bounds always yields zero area. Additivity Rule
Property allowing two adjacent integrals over the same function to be combined into a single integral spanning both intervals. Area Under the Curve
Region between a function and the x-axis, measured precisely by a definite integral. Subinterval
Division of the integration interval into smaller sections, each corresponding to a rectangle in Riemann sums. Integration
Mathematical process of finding the accumulated area under a curve, often using definite or indefinite integrals.
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