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The Meaning of Integration
Author

Thomas Rike
Organization: Oakland High School
Department: Mathematics Department
Education level

Precollege
Description

This lesson helps students understand the meaning of integration, including:
  • Integration can be used to find area under a curve. The value of the integral is an area if the integrand is always nonnegative on an interval.
  • Integrals can also have a value which is negative or zero.
  • Integrals can be evaluated by using the geometric interpretation of the integral to simplify the calculations in some cases.
  • The integral can be used to find the average value of a function over an integral.
  • Symmetry can be used to simplify integrals.
  • Integration can be used to accumulate a rate of change.
  • An integral can be used to find the value of a function at a point.
  • An Integral can be used to define a new function.
  • The integral is an infinite sum of products. (Riemann Sum)
Subjects

*Education > College
*Education > Precollege
*Mathematics > Calculus and Analysis > Calculus
*Teaching
Keywords

Integration, Area Under a Curve, Geometric Interpretation, Average Value of a Function, Symmetry, Accumulate a Rate of Change, Value of a Function at a Point, Infinite Sum of Products, Riemann Sums, Fundamental Theorem of Calculus
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MeaningIntegrationClosed.nb (46.8 KB) - Mathematica Notebook