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############ This program uses simple integration methods to integrate a function.
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############ Written by Paul Batzing as an example for FYS2140 students.
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############ DO NOT CHANGE
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from math import *
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############ END OF DO NOT CHANGE
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############ DO NOT CHANGE
############ Simple integrator that uses a sum of rectangles.
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def simple(xmin, xmax, steps, function):
    x = xmin
    dx =(xmax-xmin)/( 1.0*steps)
    I = 0
    for i in range(1,steps+1):
        I += dx*function(x) 
        x += dx
    return I
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############ END OF DO NOT CHANGE.
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############ DO NOT CHANGE
############ Integrator that uses Simpsons method.
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def simpson(xmin, xmax, steps, function):
    x = xmin
    dx =(xmax-xmin)/( 1.0*steps)
    I = 0
    for i in range(0,steps):
        I += dx/6.0 *(function(x) + 4*function(x+dx*0.5) + function(x+dx))
        x += dx
    return I
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############ END OF DO NOT CHANGE.
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############ Function to integrate, replace with the function of choice.
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def f(x): return sin(x)
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############ End of function. 
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############ Write the results to the terminal.
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print "Simpsons method with 10 steps gives: ",simpson(0,pi,10,f)
print "While a simple riemann sum with 1000 steps gives: ",simple(0,pi,1000,f)
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############ End of write to terminal.
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