alright, so back to another year of blogs... YAY :D
haha, anyways. this week we took 3 tests. oh my lord, yes i know.
one on l'hopital's rule, one on basic integration, and one on integration by parts. i did great on the first one, hopefully i did good on the other two, too. :)
ok, so let's go over some integration by parts.
first you need to find your u and your dv.
usually your u is whatever can be reduced.
then after that, you find your du and your v.
*remember sometimes your dv can be your dx and your v would then become x.
then you simply plug into the formula and integrate.
oh .. & the formula is
uv - S vdu
*p.s. - S is the integration symbol
EXAMPLE:
S xsin2x dx
u = x v = -1/2cos2x
du = 1 dx dv=sin2x
x-1/2cos2x - S -1/2cos2x
=> your answer would be...
-(x)1/2cos(2x) + 1/4sin(2x) + c
easy right? yeah. just wait til you get to the hard ones. lol OH & there is chasing the rabbit. this happens whenever you integrate something using by parts twice, and you end up with the same thing you started with in the original problem. then you simply set it equal to the original and solve it like that.
Another aspect of calculus bc that we reviewed this week, which i'll review briefly, is l'hopitals rule.
this is whenever you try to find a limit of something, but it's in indeterminate form... then you have to use l'hopitals rule.
which means you take the derivative of the top of the fraction and the derivative of the bottom of the fraction... SEPARATELY! no quotient rule. then plug in & solve.
but, you must make sure that it is in fraction form.. because you cannot use l'hopitals rule if it is not.
alright, well that's all for now.
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so, since everyone commented on everyone else's but yours..i'll give you some helpful hints.
ReplyDeletefor starters, lets go with wallace's formula..remember if the exponent is EVEN: you start with 1/2 and multiply fractions till you get to the exponent, then multiply by pi/2.
:) thought this would be helpful, boo!
Also, i almost forgot..
ReplyDeletewhen the exponent is odd, you do the same thing except you don't multiply by pi/2..you just leave the fractions regularly.
also, make sure when you bi-part, if you have a e and a trig function, chances are it IS gonig to be chasing the rabbit