Struggling in Calculus II? Need study tips for integration and substitution?

[justPAB]

Hello everyone. I recently started taking Calculus II this semester at my community college and I am having a hard time. I didn't do very well on the first exam and now we are getting into Integration by Parts, Trigonometric Substitution, and Partial Fractions. Does anyone have any tips on how to study for these subjects? I am doing a lot of problems but sometimes I get stuck. Quite frankly, the material is tough, and my professor rushes through it all at 120mph, because our class is M-Th for 1 hour. I don't really understand and feel as if I'm falling behind. I would love to have a one on one tutor; but I can't find one. What can I do? I need to pass this class for my major.

 

[Contingency]

If you just want to understand the technique, try http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

 

[Melon Knight]

I found that what helped me the most with Calc I-III was doing as many problems as I could, especially tricky substitutions, hard integrals, etc. as there's a lot of stuff they can throw at you when it comes to integration by parts, trig substitution, etc.

Eventually you would have done enough of them to see most of the tricks that may surprise you on a midterm/final.

This would definitely depend on your course. My prof followed Stewart's textbook so if you practised doing the exercises at the end of each chapter and knew the assignments inside-out, you were set for the final.

My advice would be practice as much as possible and try to figure out what your prof will put on the exam, so know the assignments and study them for patterns.

 

[retro10x]

I agree with Melon Knight, the more problems you practise, the more prepared you will be.

However if you don't yet understand the material, start by following the examples in the textbook or if you have a solution manual, work through some problems with it. Try to solve the easiest straightforward problems first, and then practise applying the technique to harder and harder problems until it feels like clock work.

 

[justPAB]

Thanks guys, I really do appreciate the help. I met with this guy today, and I paid him to tutor me for a couple hours; he was just working examples and some of the problems in my book. I was able to follow along, but once I try to work them out alone, I freeze. I'm doing a lot of problems, I try to practice as much as I can. My fear is that I don't know when I'm doing them wrong, at least with the owners manual I can check myself, but even with that, I still work them wrong from the start. I feel like I'm cheating myself when I look at the solutions, because for example: I start a problem, work through it, find out it's wrong, then I try to correct it using the solutions manual, and I feel like I'm cheating myself.

I guess I'm just worrying too much about it. I will devote all day tomorrow to do all the examples in the first three sections of chapter 7 in Stewart's 7Edition. Then I will try to work the problems.

What bothers me is that there is no set of steps or a set way to start the problems; and working them out. I mean, sure, if you have a problem that you have to start off using trig sub, then using by parts, then using u-sub, that is easy.. if you know when to apply the technique... lol...man I'm stressed! lol, well I do appreciate all the help! Thanks so much for the insight, and I will follow your advice!

 

[QuarkCharmer]

Put the solutions manual away. Get some problems out and try working them. Work them as long as it takes! Try everything you can possibly think of. If you can't immediately see the solution, try every manner of substitution you can think of and see where it leads, work them out until you deem them unsolvable by that means. Use partial fraction decomposition to try to break them up into separate integrals, try adding a constant and then subtracting it in hopes that it will allow you to do some factoring, complete the square frequently.

Just give it all a try. Work every idea out to completion. I used to be working about 5-6 integrals at a time, replacing the problems when I figured one out, and sometimes it would take me a day or two (few hr's a day) to solve some.

Calculus 2 integrals remind me of crossword puzzles. I say this because it's very difficult to solve some of the crossword puzzles unless you know the little "tricks" that they commonly use in phrasing the questions and stuff.

It's really all about practice. Calc 2 takes many people several hours a week. I know it took me much more than that "spend 3 hours outside of lecture" recommendation.

 

[jk3]

I struggled quite a bit in Cal II compared to Cal I. It took me a while to realize what my problem was. The teacher would usually be writing on the board very fast and I would just focus on copying it in time. And then when I got home I would try doing the homework problems and I would get stuck if they're even slightly different from the exercises I've previously done. I never actually took the time to understand the concepts and how the different techniques worked. I was thinking of them as some sort of mystical tools that just worked.

So I spent a lot of time before the final exam reading the textbook and going over the simplest problems. After a couple days, it just clicked. Afterwards, the questions were much easier because I actually understood what I was doing when I used a technique rather than just applying "steps 1-5".

Aside from the Stewart textbook we were using, there were two other resources that I found very helpful. The first is the same site that Contingency sugested (Paul's Online Notes). The second was a book I came across by chance in my college library: The Calculus Lifesaver (https://www.amazon.com/Calculus-Lifesaver-Tools-Excel-Princeton/dp/0691130884)

Good luck!

 

[justPAB]

Thanks guys! I am honestly going to try everything you guys are telling me. I will not stop until it "clicks!" I don't know how to thank you for your help! I really appreciate it!