sorrryyyy i missed post 3. i fell asleep before i did it, haha. anyways...
this week in calc we learned partial fractions and went over more trig sub! yayyyy. and we learned about integration tables on friday. which is pretty cool that all you have to do is plug it into a formula.
partial fractions is used when you pretty much have no other choice. and it has to be fraction. and your top degree is smaller then your bottom degree.
becuase when your top degree is larger than your bottom degree, you would use synthetic division, which may i say makes life so easy. haha
anyways, here's how you do partial fractions...
1. you factor the bottom.
2. you do a/first term, b/second term, c/third term..etc & set that equal to your equation****
3. you then do common denominator and get rid of all the fractions.
4. you plug in CONVENIENT x values.
5. solve for a, b, c, d and what not.
6. then you go back to step 2 and plug in all the numbers you got.
7. integrate & solve
****now there is a tricky part for step two. if you have something squared when you factor. like x^5/(x+1)^2
you would do this
a/(x+1) + b/(x+1)^2
... and if it was cubed, or to the fourth or whatever, you would go all the way up to that degree.
ALSO, if you have something inside of it squared after factoring.. like this
x^5/x(x^2+1)
then you would put the term that has a squared in it like this...
a/x + (bx+c)/(x^2+1)
and you would do that for whatever letter you are at... for example if you already had an a & b, you would do cx + d/ whatever.
get it? k good :)
can someone go over synthetic division again. for some reason i keep forgetting it.
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synthetic division is used when the degree of the top is greater than the degree of the bottom.
ReplyDeleteSo if i have (x^2+4)/(x-4)
you solve the bottom for x and put that number in the box. So 4 goes in the box this time.
then you write the coefficients of the top....drop the first one, multiply it by 4 and add it to the next one and so on....the numbers you get afterwards are your coefficients starting one degree lower than before. if you have a last number other than zero, it goes over x-4....