Riemann Integration

The integral of a function over an interval is approximated by "Riemann sums" with the limit of these sums being the exact integral. On this page you can experiment with different types of Riemann sums to see how closely they approximate an integral.

  • f(x) =
  • Left endpoint, a =
  • Right endpoint b =
  • mesh size:
  • Mesh Type:
    • Uniform spacing
    • Random spacing
    • Chebyshev zeros
  • Evaluation Rule - for the height of rectangles:
    • midpoint - value of the function in the middle of each subinterval
    • left endpoint - value of the function in the left endpoint of each subinterval
    • right endpoint - value of the function in the right endpoint of each subinterval
    • random - value of the function at a random point in each subinterval
    • trapazoid rule - connect points on the graph at each mesh value

Results


_

Area of the shaded region:

Exact value

_= _ Created by webMathematica _

Ken Levasseur
Mathematical Sciences
UMass Lowell
Kenneth_Levasseur@uml.edu
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