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let me moan again about Trig


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She first showed us this insanely convoluted way to do some of them.  I think the point was to show us how it works rather than just have us memorize a formula.  THEN she showed us the formula.  I did bother to go through the trouble to practice the convoluted way.  But to my relief it's not going to end up being THAT hard each time.  LOL

 

Part of it is just not knowing all the trig identities and that sort of thing.  She does let us use cheat sheets for that though.  I just wish I REALLY understood that stuff.  Not like I ever use it or will ever use it (not to have THAT sort of attitude about it, but it's the truth). 

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She first showed us this insanely convoluted way to do some of them.  I think the point was to show us how it works rather than just have us memorize a formula.  THEN she showed us the formula.  I did bother to go through the trouble to practice the convoluted way.  But to my relief it's not going to end up being THAT hard each time.  LOL

 

Part of it is just not knowing all the trig identities and that sort of thing.  She does let us use cheat sheets for that though.  I just wish I REALLY understood that stuff.  Not like I ever use it or will ever use it (not to have THAT sort of attitude about it, but it's the truth). 

 

What is "the formula"?

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Ok basically if you have an integral in a specific format it equals a specific thing (being very general).  First she had us solve these integrals by drawing a triangle, figuring out various parts (deriving...etc.), substituting that in, calculating, then writing it with the original parts (better if I could give you a specific example, but trying to type that out isn't so easy).  THEN she basically said, oh you don't need to do all that for many of the problems.  If you see this format it equals this.  OR if you can get the original problem into that format using substitutions, you can also use the same "rule".  So the first method is good to know because there are instances where the easier (more formulaic way) doesn't work, but there is a lot more to remember!

 

I hope that makes some sense.

 

 

 

 

Edited by SparklyUnicorn
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I do this to my kid on purpose.  "What, I don't know what you are talking about.  Could you explain this? Again...please...I'm just not getting it." 

 

Forces him to study.  :laugh:

 

Sorry, I did not mean to be dense, I just honestly did not know what you meant.

I know now. Trig substitutions are so cool. I felt compelled to derive the integral right after Caroline posted, and it was fun. 

Edited by regentrude
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Sorry, I did not mean to be dense, I just honestly did not know what you meant.

I know now. Trig substitutions are so cool. I felt compelled to derive the integral right after Caroline posted, and it was fun. 

 

Nah. I am not very good at using the most specific terminology.  So it's in large part that I cannot explain it so well.  I'm working on that!

 

After dong several it did start to feel puzzly.  The difficulty for me is I'm weak on some of the trig concepts (so I basically have to use a cheat sheet).  I suppose if I keep doing them I'll eventually remember those things.

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Integration is a lot more of an art than an exact science. For derivatives, there are very simple rules, but there is no guarantee any integral can be calculated by elementary means at all. It is a lot like puzzles.

I totally agree! This is my first year teaching calculus 2 in a while and I am loving all of the great integration techniques I am teaching.

 

One fun thing, my students have AP Physics the period before they have me for calculus. They are learning about drag forces in physics, and we are doing the differential equations in calculus class.

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You will remember. It is at first such a strange thing to do the sin theta substitution because the function in the integral has nothing to do with trig - that seems like wizardry. And I recall there are lots of substitutions where you use tan (theta/2) - THAT seems completely bizarre.

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Integration is a lot more of an art than an exact science. For derivatives, there are very simple rules, but there is no guarantee any integral can be calculated by elementary means at all. It is a lot like puzzles.

 

That's not comfortable when learning it.  LOL

 

I am good at being methodical.  Having to break from that to deal with fuzziness is what I find very challenging. 

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That's not comfortable when learning it.  LOL

 

I am good at being methodical.  Having to break from that to deal with fuzziness is what I find very challenging. 

 

Yes, I understand. But that is simply what it is. There are no clear cut rules, because integration is very strange. With experience, you will be able to guess more easily which integrals require which tool box - trig substitution, partial factions, or integration by parts. 

 

At MIT, they have an Integration Bee. that's all integration puzzles, some are wicked.

 

The good news is that you will mostly do this in this class only; if you apply integration to problems, there used to be thick books full of integration tables, which you now look up on the computer.

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