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Introduction to approximation techniques other than vertical strips (Trapezoid Rule and Simpson's Rule).
Derivation of the Trapezoid Rule for approximating Riemann integrals.
Derivation of Simpson's Rule for approximating Riemann integrals. Worked example using Trapezoid Rule and Simpson's Rule.
Finding Riemann sums with fixed widths using the leftmost, rightmost, maximum, and minimum argument in each strip, including comparisons of each and an applet for finding the leftmost and rightmost Riemann sums for a function.
Definition of this rule for approximating the area under a curve, including a measure of the error for this method compared to the actual value of the area.
Definition and formula for this rule which uses quadratics to approximate the area under a curve, including a comparison of this and the Trapezoid Rule. Also includes an applet for finding the area under a curve using the rectangular left, rectangular right, trapezoid, and Simpson's Rule.
Using extrapolation to greatly improve the accuracy of approximations using the Trapezoid Rule or Simpson's Rule.
Computing the right endpoint Riemann sum of an integral and then using that answer to evaluate a limit.
Three problems which involve evaluating Riemann sums and integrals.
Finding the approximate value of an integral using each rule with two subintervals.
Estimating the number of hits a player got in a month using the two rules.
Using Riemann Sums, the Trapezoid Rule, and Simpson's Rule to approximate a definite integral.
Estimating a definite integral of the sine-squared function using three intervals of the Trapezoidal Rule.
Seven questions which involve using sigma notation for sums, computing Riemann sums for definite integrals, and evaluating limits by relating them to Riemann sums.
Five questions which involve approximating integrals using Riemann sums, the Trapezoidal Rule, and Simpson's Rule.
Applet which uses the Left Hand Rule, Right Hand Rule, Trapezoid Rule, and Simpson's Rule to approximate the area under a specified curve.