So, lets get this thing going again. First i'll give a little summary of things I did this past week. We went over lo'hospital's rule, integration, substitution, bi-parts, trig integration, and i think there's one more thing that just isn't clicking this moment.
So since this week was basically a review, let me touch on everything we did. Kinda like a re-review.
So, lets do some reviewing...
LO'HOSPITAL'S RULE:
1. This deals only with limits..so if you don't have a limit, dont do this!
2. Plug in the number the limit is approaching into the equation and make sure you get an infinitave..such as infinity/infinity, zero/zero, infinity/zero, zero/infinity.
3. Next, you need to take the derivative of the top, and the derivitave of the bottom.
******NOT QUOTIENT RULE, JUST TWO DERIVATIVES.
4. Plug in the number the limit is approaching
5. If you get another infinitive, repeat.
INTEGRATION:
*So, i know this is a little review, but don't laugh...you mess up on these sometimes too!
1. You know it's an integral when you see the "s" looking thinggyy.
2. Add one to the exponent
3. Multiply the coefficient by the recriprocal of the new exponent.
If indefinite, be sure to include +c, if not, solve.
So, these are the two topics that i was most confortable with my quizzes.
Now, the things i'm pretty sure i didn't do good on, bi-parts and trig substitution..
These two topics just don't click in my head. Any suggestions on how i should study thesee things?
Also, how do you tell if its biparts or trig sub..?
What would you do for S xarctanx?
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So by parts or trig sub?
ReplyDeletethe way i do it is this. You have to memorize your boxes for trig sub. if it looks like any of those, then obviously do trig substitution. HOWEVER...I have made the mistake numerous times and done by parts...when in actuality all I had to do was us the identities and do regular substitution. Just think of by parts as a last resort type of thing. Good luck!!
To tell whether you have to use trig-sub or by parts depends on what type of problem you are given.
ReplyDeleteIf you can see right away in your problem that you have two terms, one that you can easily take a derivative of and one that you can easily integrate, then definately use by parts. By parts is usually used when you have either just one term of trig or none at all. By parts deals with lowering x powers to make the problem at hand simpler.
Trig substution is usually used when you have two terms of trigonometry. Use your trig. formulas from advanced math and the integration formulas we have been using the past week for this type of integration.
Hope it helps,
Ryan
By Parts is all about the formula dog: uv - Sdu
ReplyDeleteEXAMPLE:
Sxe^x
u=x v=e^x
du= 1 dv=e^xdx
*u is something you want to reduce and dv you need to be able to integrate
*now plug into your formula
xe^x - Se^xdx
*now integrate the second part..sometimes this will involve doing bi parts again, substitution, or it may just be a straight integral like this example
=xe^x - e^x +C
*don't forget +C !