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Continuous Functions Are Integrable

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number of rectangles
23
function
x/2
2
x
/2
3
x
/4
log( x + 1 )
sin(x/5)
This Demonstration illustrates a theorem from calculus: A continuous function on a closed interval
[a,b]
is integrable, which means that the difference between the upper and lower sums approaches 0 as the length of the subintervals approaches 0.
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