This section contains documents created from scanned original files and other
documents that could not be made accessible to screen reader software. A "#"
symbol is used to denote such documents.
Riemann integrals are introduced as a concept using the example of finding the area of a circle from the areas of N-sided polygons inscribed in the circle. Signed area (positive above the x-axis, negative below) is introduced.
Interval partitions are defined, including the concepts of mesh size and fine vs. coarse partitions.
Definition, including a discussion of partition choices when computing these sums.
Definite integrals are defined. Includes an example using the function f(x) = x.
Using Riemann sums to find the Riemann integral for the function f(x) = ex.
Using Riemann sums to find the Riemann integral for the function f(x) = xr.
Definition of the definite integral as the area under a curve, including definition of the integrand.
Definition, including the use of Riemann sums in finding the area under a curve.
Using upper sums to evaluate a definite integral.
Three problems which involve evaluating Riemann sums and integrals.
Evaluating an integral using the definition of an integral as the limit of sums.
Seven questions which involve using sigma notation for sums, computing Riemann sums for definite integrals, and evaluating limits by relating them to Riemann sums.