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Friday, January 16, 2009

Accumulation Functions Cont'd

This scribe post will be short as I hope to fully complete it tomorrow (hopefully) or Saturday (likely). Its like 2am. I think my name is George.

Today we started by reviewing the idea that an accumulation function is a composite function, with one function (the function defining limits) taking place within another function (the function we are finding the integral/area under of).

After that review, we worked on some problems. A good thing to remember is that if the integral is going from a value to your function, you want to use that inverse thingy and make it negative so you're going from your function to a value. This is on Slide 3, the second example. The integral from 2 to x is equal to the negative of the integral from x to 2, which is simpler to solve out.

After that he gave us a question that involved finding the total area under a cubic function. However, we hit a snag because nobody quite remembered how to find the roots of a cubic function! After a long demonstration and reminder about synthetic division, Mr. K gave us the roots. I highly reccomend going over the Gr 11 notes he added to the slides (Slides 6 - 11) if you dont remember synthetic division and or want to brush up.

However, after finding the roots, the solution is simple since we already know how to find the area under the graph via the integral. Be careful, as the integral = SIGNED area, meaning if you take the integral from the left most root to the right most root you'd get the wrong answer because part of that integral is negative and thus that integral would be smaller than the total area that we are looking for. In this case, because the integral from 1  to 2 is negative, when we add them together we add the negative integral instead to get the total area.

That basically sums up today's (or rather, yesterdays...) class, I'll try to expand this post to further explain the ideas we explored (yesterday) today, but as of the moment I am way too tired.

And finally because Im tired and want to go to bed, the next scribe is J-Cap (J+ME).

Good Night, and or good morning.

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