Monday, July 20, 2009

calculus - integral


This sketch explores the idea of an integral as an area beneath a curve. Riemann Sums are brought to life as the number of sub-intervals on a user-defined (a,b) interval can be varied between 1 and 1000 using a sliding parameter indicator. Comparisons can be made between right sums, left sums, midpoint, and trapezoid techniques. The user can see the errors diminish as the sum of simply calculated areas approaches the exact area beneath a curve. The sketch includes a tool for shading the region between two curves, whose arguments are 2 points followed by two functions.
Keywords: calculus, Riemann sum, right sums, RRAM, left sums, LRAM, midpoint, MRAM, trapezoid, trapezium, converge, area, integral, integration, subintervals, definite integral

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