DR. LUV

Okie dokie. The class started off with more problems with the substitution since everyone wanted a little more practice. I found it fun XD. The first problem was the same as yesterdays except we used a different "u". What I took out of this part of the lesson was...that solving these kinds of problems become very routine. They're all similar in the way you go about solving them.





Another big part of the lesson was the final answer. Mr. K emphasized that those meanies who make our exams don't include the pre massaged answers to select in the multiple choice. There's always an extra step. For example in this question, after finding the antiderivative our answer was:

2/5(x+3)^5/2-2(x+3)^3/2+C

However we need to do more with it. We must factor out the "lowest common factor" (i'm not sure what we called it...oops). For this question we can factor out a:

2/5(x+3)^3/2

So that's what they'll usually put in the multiple choice answers for the exam!





We also started some new stuff called Integration by Parts. For these kinds of questions we used the product rule and algebraically massaged it to make a rule for antidifferentiating. Now that we have an antidifferentiating rule we can follow it and choose what we'll have as f and g'. The rule of thumb is to always choose the most complicated variable that is the easiest to antidifferentiate. All that is needed is to plug in the new values into the rule. However, bookkeeping is very important once again. Keep track of all the substitutions and the signs....or else.





For the next example, we did the same steps and everything. Only difference is what we chose f to be. g'=x² because it is the easiest to antidifferentiate. (I got a little confused in this step thinking it was lnx that could be g'. But it can't since we don't know the antiderivative of it. I even had Mr. K fooled for like a full....20 seconds thinking the antiderivative for lnx=1/x, which it isn't.) Then all that is left to do is to plug in the values and voila. Oh and to factor out the "lowest common factor".

The only chit chat I remember today was Mr. K talking about some job called an...acc...something. I forget that too. But he says it's a really good paying job XD. Holy carp, since when did our scribe list get so tiiiny? ANYWAYS, next scribe will be Benchmen.