Late again. The past few weeks, we’ve taken AP tests twice a week, the calculator and non calculator portion of the multiple choice portion. Lately, it just seems that I’m overwhelmed with all of the AP tests and getting the same stuff wrong over and over. It also seems like the tests keep getting harder and harder, but B-rob said the ones we are doing right now are harder than the actual AP (I sure hope so).
In stats since Friday, Alex has sat down with the calculus side of the class and tried to go over the previous AP test as best he could. It’s helping a good bit. I had forgotten a few things since B-rob left and since she sat down and went over our APs with us. One of the things I realized is that you’ll use substitution more times than not. Alex was going over a problem Friday in class that I didn’t even know substitution was supposed to be used for. I thought I could just take the integral normally, but I forgot to put a 1/8 outside of the problem. In many integration problems I’ve been seeing that I haven’t been getting the right answers, I guess this is why. I’m looking for it right now, but I can’t find the problem, but I think it went something like this:
the integral of cos(8x) from 0 to 3
For this problem, I just would’ve tried to find a way to do it without using substitution, but Alex did. He set u = 8x and du = 8, then since the 8 wasn’t origionally in the problem, he put it in, and put a 1/8 on the outside to balance it out. This is technically substitution, I was just forgetting this step in my head.
I’m doing better with particle problems, but things I’m confused with are problems like integrating (sin(x))^2
integrating sin(x)^2
ReplyDeletefor the exponent. add 1 and then multiply by its reciprocal...
(1/3)sinx^3
then.. next is sin(x)
the integral of sinx is the complete opposite of sinx.
which would be -cosx.
then your final answer would be -(1/3)cox(x)^3
You can't integrate sin^2(x). The derivative of sin is not in the problem. You have to use the identities. See an earlier post.
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