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// This contains routines for integrating a function numerically using
// interval techniques.
// This function takes an anonymous one-argument function f and numerically
// integrates it over n steps from lower to upper. The result is an interval
// that should be guaranted to contain the true value of the function.
IntervalIntegrate[f, lower, upper, steps] :=
{
// Make sure steps is an integer or this will fail.
steps = ceil[steps]
stepsize = (upper-lower) / steps
sum = 0 f[lower] stepsize // This is necessary to get the units right.
min = lower
max = lower
// By counting for a guaranteed number of steps, we can avoid roundoff
// error and "missing" and endpoint when using floating-point boundaries.
while min < upper
{
min = max
max = min + stepsize
if (max > upper)
max = upper
width = max-min
mid = (min + max)/2
int = new interval[min, mid, max]
/* println["int: $int"]
println["f[int]: " + f[int]]
println["width: $width"]
println["sum: $sum"]*/
area = f[int] * width
// println["$int\t$area"]
sum = sum + area
}
return sum
}
// This equation tests the integration with an anonymous function and returns
// an interval.
//IntervalIntegrate[{|x| sin[x]/x}, 1e-10, 2 pi, 100000]
// This represents the light from a long cylindrical lightbulb
//IntervalIntegrate[{|h| 1000. lumens/ft / (h^2 + (12 in)^2)}, -1/2 ft, 1/2 ft, 10000] -> lumens/(foot^2)
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Alan Eliasen was born 19965 days, 13 hours, 15 minutes ago.