/sci/ - Science & Math

Are you an engineer?

So you're upset that your professor is trying to explain to you how things work rather than just telling you to memorize it at surface level?
You must be an engineer.

No, just a college student. Undecided major so far.

And I wouldn't mind learning why these things work on top of how--if I were a math major. Outside of that scenario, exploring mathematics for the fun of it seems pointless to me.

does he by any chance just want you to derive the answers, you know, like you should be able to?

and i have no idea why you don't just type them into wolfram alpha, but it's probably for the same reason you can't do them anyway.

This looks like integration by parts to me

He wants us to integrate the answers, which I can't, because his method of teaching involves standing up with the intention of saying something instructional while illustrating it on the board, then skipping down some math-related bunny trail. Afterwards, he assigns us homework as if we've learned something. I've basically been trying to teach myself calc II from the book.

It's not going so well.

just fucking do it

it's good practice; you can never get enough practice with calc

Typing them into wolfram alpha yields--exactly what's on the page. What he wants is the stuff in between.

>>3234295

Theres a 'show steps' option I believe

It might be good practice if I can do it, but I'm pretty sure staring at a problem for half an hour with no idea of what to do doesn't help anyone.

Calc 2 is considered by most to be the hardest in the series. It's because the method of solving any given integral is very infrequently obvious. You typically are forced to use a combination of integration by parts, trig substitution, standard substitution, and more. The reason your teacher wants you to do all these problems, and understand why they work the way they do, is so that you can identify which techniques need to be performed on which integrals. It's not even about the why. They're complicated enough that to do them, you need to at least be familiar with each technique in a thorough manner.

What I'm trying to say is, if he just threw an integral up and said "We solve this one by using integration by parts" that wouldn't help you, because you'd have no grounding on when to use that again and when not to. You'll waste a lot of time trying to solve an integral by hand only to realize it's improper and you needed to take a limit somewhere without this kind of training.

Lovely.

(This is where my rant against integrals would go if I could summon the energy)

Do you know where I can find some good instructional material, then? Something with a list of my various options/possible strategies?

>>3234295
if you can't work that out, i have no idea how you managed to figure out how to post on /sci/

i hope you fail, because your lack of being able to do anything for your self is pathetic.

OP, I'm sorry you're having trouble with Calc II. I hated the course and scraped through with a C+. I'm currently in differential equations for the second time (I failed the first time) and I was able to pass Calc II with this website.

http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

It helps for Calc II and Calc III (though it isn't that great for diffeq).

Good luck to you; just powerhouse through it!

Math gets alot better later on.

>>3234313
Your textbook.

I'm really sorry, I know that's not the answer you wanted to hear. I'm a math major, and let me tell you that I fucking -hated- calc 2. It was the most boring class I ever had to take. Math has always been interesting to me, but calc 2 was the worst. You have no option except to slog through it. My recommendation is that you attend office hours and you do a LOT of practice integrals.

In general, though, there's a list of about 15 to 20 integrals that you'll want to flat out memorize, because you'll frequently be able to reduce to them. You'll also want your trig identities memorized; the Pythagorean identity as well as the half and double angle formulas. With these tools under my belt, first I try to simplify any integrals. Then I look for obvious substitutions, working my way into the trig if I see something related to those substitutions. It sucks, but there are no hard and fast answers.

Wolfram alpha will go through the steps of integration. I believe all of these can be solved with u-substitution where u=ax+b and du=adx. Not too bad. Here's an example (first integral):

http://www.wolframalpha.com/input/?i=int+x%28ax%2Bb%29^n+dx

>>3234324

Also, I should say that I have no idea what's going on in your picture.

Srsly, fuck that shit.

>>3234328
as a side note, when I say memorize, I mean the basics, like "e^x dx = e^x" and "1/x dx = ln|x|" ; the kinds of integrals that nobody expects you to show work for. Not the integrals that he's probably asking you to do.

Actually, as a fun bonus (and by bonus I mean actual question representing a portion of the grade) he told us to find the derivative of e^x.

>>3234238
Stop studying maths, you'll never make it in mathematics. I mean it in all seriousness, if you're not interested in why things work you're not interested in mathematics, you'll have no talent or taste for it.

>>3234398
Do integration by parts, find integral is e^x, differentiate integral, get e^x. There's your free marks.

"Who cares"
um... i've went over my calculus book 3 times just to make sure i know WHY things work. Its very helpful and saves a lot of hassle. Its also pretty neat sometimes and can help you improvise ways to incorporate math into your own life.

Yeah, it really looks like math is not for you if you think knowing the theorems is sufficient while learning the proofs is superfluous. Perhaps you should spend your time on /lit/.

>>3234458
Or study something ending in -ology.

>>3234463
topology?
melborp?

Very nice. Yes, I prefer reading, music and computers to math any day, but those don't offer too many jobs. Let's see: I can become an English teacher for kids who hate my class because I make them write (ugh), I can become a professional singer (no, I'm pretty sure I can't), or I can get a Computer Science degree. (Hey, those computer guys make good money, right? I guess I'll do that.)

Oh yeah, just one little problem: it takes nearly as much math as the Physics degree I came into college so sure I was going to do. Hm.

>>3234482
Business or law offers more jobs than anything math related.

On the other hand, geology was my second-favorite subject in high school. Maybe I'll make a career...looking at rocks.

>>3234486
No, it really doesn't. There are a small minority of business and law people who make a TON, but the rest are poorfags.

It's best to stick with engineering fields. If you want to pursue pure science or math, go ahead, but be prepared to be an academic.

>>3234491
Check the actual statistics. Remember that even if you are employed it does not mean you are employed in your own field. The sad truth is there aren't many engineering jobs out there. A good number sure, but none of them are for retards.

>>3234497
You're fucking retarded. 80% of the people in my EE department got ENGINEERING jobs directly out of college. The remaining 20% either went to grad school or did something else. Very few or none were unemployed. (Maybe this is not the same for a shit-tier school.)

Obviously the same cannot be said for the business kids, most of whom end up as bank tellers because their 2.7 GPA wasn't good enough for an MBA.

those are easy integrals.

supposing a, b, n are constants:

let u = ax + b OR (u-b)/a = x
du = a dx.
dx = du/a.

so:

1/a int ((u-b)/a) * u^n du

do shit, play with it, etc. all of them can be solved through these methods.

>>3234508
because bank tellers are horrendously underpaid and have no responsibility, amirite?

>>3234497
%80 is not a good number after years of education and a debt. And EE is one of the better fields.

>>3234512
Except this guy. I like this guy.

It's either integration by parts or some sort of faggot substitution. Those are the only two tricks.

>>3234482

> those computer guys make good money, right?

They actually don't, that's the funny thing about it.

>>3234549

SHUT UP DON'T RUIN MY DELUSIONS

>>3234544

And yes, "faggot substitution" pretty much sums all of these problems up perfectly.

I'm pretty sure 11 is wrong, it should be n+2 in the exponent on the right hand side.

Just keep using

u = ax+b

and hence du = a dx over and over until something falls out. If that doesn't go anywhere, try u = sqrt(ax+b) =(ax+b)^(1/2)

Yeah, I've been using u=ax+b. It's working, except that on 8 I managed to drop a b/a^2 just before the end.

>>3234575
Wow, I didn't even see that. I was confused for a bit until I opened up the image. Due to a problem with resizing, that plus got blurred to a minus. So the equation is correct, but you win an internet anyway for good math.

>>3234593

Yeah, that should do it. The usual guide is to substitute the most complicated looking part, within reason. Like u = ax + b isn't too bad and leaves you with sqrt(u) which also isn't too bad, but u = sqrt(ax + b) would make things look simple, but would be too hard to work with.

You want a real "who cares" feeling, try taking a course in computer systems. The lecturer is so dam excited about the way computers work at the bare metal level, registers flipping all over the place, but seriously who gives a fuck.

Now pure math, THAT'S where it's at.

>>3234487
Are you suggesting that geology isn't a great career choice? Because you'll be surprised...

>>3234698

Actually geology is the best. It gives you a whole new perspective on the world around you, and there's a lot of work to be had.

>>3234703
>study geology
>be pidgeonholed into a job relating to oil

>>3234705
>Study anything
>Be pigeon-holed into job related to it

>>3234705

Not necessarily! You might get work doing soil surveys for septic tanks.

>>3234531

Actually, yes they are underpaid, at least where I live.

Most math majors wind up as teachers because they get fired from real jobs. Your instructor sound like the typical worthless math major that knows nothing of applied math. Lots of these pricks get mad when you ask about applied problems. They also seem to not know shit about Matlab/Maple/Mathematica.

>>3235121
Where I'm from the opposite is true, most of the single maths majors are applied, and if you ask them a real maths question they just stare blankly. I don't see what's so wrong with studying maths out of a desire to study maths. Most double maths majors are good at maths and at the game of applying mathematics to boring things.