Copy of Approximate Integration

To approximate the definite integral we split the region up into many thin slices. For each slice we may approximate its area using rectandles, in which case we could either use right-endpoints, left-endpoints, or midpoints to work out the height of the approximating rectangle (seen in blue). We could also use trapezoids to approximate each slice (seen in red). Drag the slider labeled n to increase the number of slices used.[br][br]On the other hand, we may group two sub-intervals together and use a parabola to approximate the top of the slice. This is a technique known as Simpson's Method (or Simpson's Rule).[br][br]If you wish to change the function f, say to sin(x), then just type f(x)=sin(x) in the input field at the bottom of the applet.
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[/img]
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Information: Copy of Approximate Integration