                    Title    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   Downloads     MeaningIntegrationClosed.nb (46.8 KB) - Mathematica Notebook       