Its a start to a new unit and a review of an old, we began by going back to this graph here,

during the time when we began to learn about integrals, and r sums, some time ago in October. However we learned, in today's class that we can solve an integral whether or not the width of the bars or interval are the same (ex fat. thin) as long there are an infinite of r sums them that will squish them together within the graph.

As you see in this picture the bar/r sums have the same width (the reason why we use uniform intervals is to make it easier to solve by hand)

Here is a quick refresher

To find the left hand sum you add all the lengths of the line highlighted in purple, or the length of the left side of each rectangle, then multiply it by the width (if the width is the same through out the graph)

Or you can find the area of each of the striped rectangle and add them together either way you'll get the left hand sum

Also the same as the left hand sum where you add the the highlighted areas together or add the highlighted lengths and then multiply it by the width. Then only difference is that you do not include the length of the first rectangle, just like how the left hand sum doesn't include to length of the last rectangle.

Note: When doing the left/right hand sum you cannot use both ends of the graph!

When solving for the left hand sum = no last rectangle

When solving for the right hand sum = no first rectangle

On a new note when finding the area of the graph it can be found by adding the left and right hand sum, divide them by two and then multiply it by the height, or the width in this matter, which is also the same as finding an area of a trapezoid.

((Left hand sum + Right hand sum)/2) w = area of a trapezoid

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And that is what we mostly did in class today and we manage to get up to a brief introduction of the Fundamental Theorem and finish 2 questions on the smart board, but we will continue in tomorrow's class.

And I choose Zeph to be the next scribe!

## Thursday, January 8, 2009

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