SparklyUnicorn Posted November 2, 2017 Share Posted November 2, 2017 integrals with trig substitution WOW these hurt my brain....very very badly.... I don't know if I'll get through this. LOL 1 Quote Link to comment Share on other sites More sharing options...
.... Posted November 2, 2017 Share Posted November 2, 2017 Ugh! We're almost there! :001_unsure: Are you still using Saxon? I told dd15, "Let's just get through precalculus/trig and we'll stop there. Lol." 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 2, 2017 Author Share Posted November 2, 2017 So my advice to you is REALLY learn the trig stuff. I'm talking about me and the class I'm taking. DS is also taking the same class, but he isn't moaning. LOL 3 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 I think I'm getting it. Weeeee... LOL Quote Link to comment Share on other sites More sharing options...
JoJosMom Posted November 3, 2017 Share Posted November 3, 2017 Trig stinks! And integrals with trig substitutions are the WORST! Poor Sparkly Unicorn! Here, I made these for you . 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 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). Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 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"? Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Well not "formula" exactly. But rules I guess. Arcsin rule, etc. First she showed us how to figure these things out and it had what seemed like 10 steps. Quote Link to comment Share on other sites More sharing options...
.... Posted November 3, 2017 Share Posted November 3, 2017 So my advice to you is REALLY learn the trig stuff. I'm talking about me and the class I'm taking. DS is also taking the same class, but he isn't moaning. LOL Oh, you guys are taking a class together. That's awesome! 1 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted November 3, 2017 Share Posted November 3, 2017 What is "the formula"? Stewart’s Calculus has four pages of formula at the end of the book. 3 page pdf uploaded by a lecturer https://math.boisestate.edu/~wright/courses/m333/IntegralTablesStewart.pdf 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Arcsin sounds like the name of a drug. For some sort of weird skin condition. No clue why I think that...but yep. 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Stewart’s Calculus has four pages of formula at the end of the book. 3 page pdf uploaded by a lecturer https://math.boisestate.edu/~wright/courses/m333/IntegralTablesStewart.pdf Whoa...I printed it out. They have some of that in the book, but not all of that in one place. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 Stewart’s Calculus has four pages of formula at the end of the book. 3 page pdf uploaded by a lecturer https://math.boisestate.edu/~wright/courses/m333/IntegralTablesStewart.pdf Oh you mean integral tables? Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 Well not "formula" exactly. But rules I guess. Arcsin rule, etc. First she showed us how to figure these things out and it had what seemed like 10 steps. still not following, what is the "arcsin rule"? Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 (edited) 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 November 3, 2017 by SparklyUnicorn Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 sorry, I am still lost. Why do we draw a triangle for integral trig substitutions? And what is the "rule"? Quote Link to comment Share on other sites More sharing options...
Caroline Posted November 3, 2017 Share Posted November 3, 2017 sorry, I am still lost. Why do we draw a triangle for integral trig substitutions? And what is the "rule"? I think the professor was proving that the integral of 1/sqrt(1-x^2) is arcsin (x) maybe? Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 I think the professor was proving that the integral of 1/sqrt(1-x^2) is arcsin (x) maybe? Oh! THAT! Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Simple example: https://www.amazon.com/photos/share/RJVagG5UCtETjvVH50Tg6kxe301EzJipOUMUt3dyN2X/gallery/s30AdQyrRj-3HtjaeFgOsQ Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 I think the professor was proving that the integral of 1/sqrt(1-x^2) is arcsin (x) maybe? Yes! She made us do several problems this "long" way. I was thinking OMG I'm going to die if there will be several like this on the exam. :lol: Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Oh! THAT! 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: Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 (edited) 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 November 3, 2017 by regentrude 1 Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 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. 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
Caroline Posted November 3, 2017 Share Posted November 3, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 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. Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 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. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 3, 2017 Share Posted November 3, 2017 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. 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted November 3, 2017 Author Share Posted November 3, 2017 Oh yeah I like doing them. I like all of it. What I don't like is the pressure of time and tests. I know that's how it goes, but I feel rushed. Like I can't stop to smell the roses (in this case the math). Quote Link to comment Share on other sites More sharing options...
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