Area

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2

Slide 16

Area Approximation

So the width of each rectangle is

The height of each rectangle is either

or

So the upper and lower sums can be defined as

Lower sum

Upper sum

Slide 17

Area Approximation

It is important to note that

Neither approximation will give you the actual area

Either approximation can be found to such a degree that it is accurate enough by taking the limit as n goes to infinity

In other words