So, partial fractions were the main focus this week, along with sharpening our integration skills. Some things you need to remember when it comes to partial fractions, is that there are basically 4 cases, including synthetic division, that you can use when regular substitution fails, and by parts I think too. So, basically, when you see a fraction...
1. See if it can be solved using synthetic division (i.e. degree of top greater than degree of bottom)
2. If synthetic won't work, then Factor the Bottom!
Once you're dong factoring, you're gonna want to split it up with different letters over all the factors...so A B C, and so on.
However. If you have say a (x+1)^2, you have to put that particular factor over Cx+D...don't ask why, it's just the way of the gods..
So once you decide what to do after factoring, you go through and plug in numbers for x (after finding common denominators) that cancel out the other letters, till you have values for all letters (variables) used.
Once finding those values you go BACK, again, and plug those in in the appropriate places. Once you get that, then you FINALLY integrate. Yayy!! finally! (Most of the times you should get a lot of natural logs...just saying. Got it? good.
Okay...a question...what the heck is this integration table thing?? Unfortunately I was absent that day, so I was unable to get a good explanation....so if someone could do a problem or two and explain each step, it'd be much appreciated....:DD Thanks!!!
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okayyy, well i can't do a problem. but i can tell you this. the integration table is located on page A21. which is alllll the way in the back of the book.
ReplyDeletei'm not exactly sure in which cases you use it, brob actually said it probably won't be on the ap. but, i know to use it when the directions say "use your integration table".
whenever you get a chance go look at them, it's about 3-4 pages long of formulas. you just use them for whichever case fits. sorry i couldn't do an example!