Question: What is the Riemann Sum

Let we have a function, f(x), and want to approximate its integral from x = a til x = b.

Divide the interval [a,b] into n equal (not necessary equal) parts.

Let one of the part, i,  is from x(i) til x(i+1).

Let us draw a tangent to the curve in this part, i, by the command:

Tangent(f(x), x=(x(i)+x(i+1))/2)

we may find the area under this tangent and in this interval through the command:


Thus in ths limit:

the original area is equal to the sum of these areas.

How to derive an expression with maple for it?


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