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Calculus Help (Read 364 times)

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Fire Mage

#1 April 07, 2008, 09:46:05 pm

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I have no real clue where this would go on the forum, or if it should anywhere, but I need someone to explain a problem to me. I can't search the internet or look in a book (particularly because it'd be hard to find the problem and also I hate book-explanations). So if someone here can help me quickly...at least if there is someone here who understands Calculus. So...yeah. Being in Calculus (part one) in 11th grade is kind of easy, but this one problem has got me. Maybe I'm looking at it wrong.

I have really no clue where to go on this problem on my quiz review sheet. The problem is:

Code:[Select]

Find the definite integral from 0 to 1 of:

(x-1)/(x+1)    dx

I feel kind of stupid about the problem, and maybe I'm not looking at it right.

Anyway...uh, yeah...can whoever sees this just leave this here? Hopefully someone here can help me, because I need human explanation.

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GirlBones

#2 April 07, 2008, 09:57:00 pm

I will.
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things i learned from this topic: i don't remember a damned thing from my calculus class.

seriously - i got a good enough grade in that class for college credit, but looking at your post, i literally do not know what a single damn bit of that means.

boop oop a doop

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AdderallApocalypse

#3 April 07, 2008, 10:00:34 pm

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∫{0..1} (x-1)/(x+1) dx
Split into two integrals:
= ∫{0..1} x/(x+1) dx - ∫{0..1} 1/(x+1) dx

First integral:
∫{0..1} x/(x+1) dx
Let u = x+1 → du = dx and x = u-1
= ∫{x=0..1} (u-1)/u du
= ∫{x=0..1} 1 - 1/u du
Split into two integrals:
= ∫{x=0..1} 1 du - ∫{x=0..1} 1/u du
= u - ln|u| {x=0..1}
= (x + 1) - ln(x + 1) {x = 0..1}
= [(1 ][/(1] - [(0 ][/(0]
= 2 - ln(2) - 1 + 0
= 1 - ln(2)

Second integral:
∫{0..1} 1/(x+1) dx
Let u = x + 1 → du = dx
= ∫{x=0..1} 1/u du
= ln|u| {x=0..1}
= ln|x + 1| {x=0..1}
= ln|1 + 1| - ln|0 + 1|
= ln(2) - ln(1)
= ln(2)

Combining the two integrals:
= [1 - ln(2)] - ln(2)
= 1 - 2ln(2)
= 1 - ln(2^2)
= 1 - ln(4)

That should be right, if not then it can't be too far off!

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dada

#4 April 07, 2008, 10:05:09 pm

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I never had calculus. I dropped math entirely as soon as I had the chance. Now, about 6 years later, I wonder why. I was really good at math, much better than any of the other stuff I was taking.

So I bought a gigantic calculus book and started pounding away. But because I have so little time these days, I'm not very far yet!

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AdderallApocalypse

#5 April 07, 2008, 10:07:57 pm

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I hope one day to be an engineer, so I need a lot of math and science.

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Fire Mage

#6 April 07, 2008, 10:16:04 pm

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Quote from: Omcifer on April 07, 2008, 10:07:57 pm

I hope one day to be an engineer, so I need a lot of math and science.

As do I; I'm in a Science and Engineering program at my school.

Also, one quick question, can you check this:

Code:[Select]

problem >>> ∫ csc(39x)dx

my answer >>> -(1/39) Ln|csc(39x)+cot(39x)|+c

If you can understand that typing. Also, I'm going to check out your other solution, it's rather long. Bleh, I didn't hope the answer would get this long.

Finally, so this topic isn't useless, you can discuss math or something.

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Von Woofen

#7 April 07, 2008, 11:12:38 pm

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I'm taking calc this year too, and it's easily the hardest thing high school has to offer. I'm not taking the AP test, I'm just going to take it again next year and hopefully I will really learn it by taking it twice.

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Vellfire

#8 April 07, 2008, 11:15:20 pm

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I took calculus in high school and made a C (our teacher would miss for weeks at a time so uh yeah not much learning there), but because I got a ONE on the AP test it didn't count as college credit. I tried taking it this semester but dropped it because I was failing, our teacher did nothing but assign us homework then go over it (and still no one understood it because he didn't teach it to begin with). Eventually I'll have to take it for my CS major, but I'll be able to do it with a better teacher. Ugh, I just want to fucking pass calculus and get credit for it already.

Can anyone in CS or programming or anything related tell me which parts of calculus I will actually use?

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Fire Mage

#9 April 07, 2008, 11:25:55 pm

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Quote from: Von Woofen on April 07, 2008, 11:12:38 pm

I'm taking calc this year too, and it's easily the hardest thing high school has to offer. I'm not taking the AP test, I'm just going to take it again next year and hopefully I will really learn it by taking it twice.

Oh, I'm not in AP Calc. I'm lucky I guess.

I have dual enrollment, which means that it'll be split over two years for me and the kids in my program. So far it hasn't been hard to me really; the last test we took I got 105 (perfect score on it) and others didn't...so maybe it's just me.

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Mince Wobley

#10 April 07, 2008, 11:47:03 pm

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All that math formulas etc look like a lot of gibberish to the untrained eye

Play Raimond Ex (if you haven't already)

I'll not TAKE ANYTHING you write like this seriously because it looks dumb

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AdderallApocalypse

#11 April 07, 2008, 11:49:14 pm

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FireMage, your answer looks like it is correct. I might check again later, but it looks good.

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WunderBread

#12 April 08, 2008, 01:48:09 am

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Yeah, uh, taking AP Calculus this year because AP is the only kind they offer. It was either that or AP Statistics.

I should have taken Statistics.

I suck at Calculus. Hard. Like, I would be failing that class if our teacher didn't give such ridiculous grading curves all the time, and a 50-point project that is basically extra credit. That said, calculus is supposedly easier when you take it again (or so people tell me), so maybe I'll get it in college. Then again, maybe not. Actually, probably not at all.

I think I'm going to be a chemical engineer (chemistry was actually one of my good classes), so knowing which parts of Calculus I'll actually need to use would be beneficial, too.

Quote from: Inri Cheetos on April 07, 2008, 11:47:03 pm

All that math formulas etc look like a lot of gibberish to the untrained eye

Hell, to the trained eye it looks like gibberish, too. I think it's because our teacher teaches it a completely different way, though. I'm totally getting a 1 on the exam. No questions asked.

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Fire Mage

#13 April 08, 2008, 02:59:34 am

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Quote from: WunderBread on April 08, 2008, 01:48:09 am

Yeah, uh, taking AP Calculus this year because AP is the only kind they offer. It was either that or AP Statistics.

I should have taken Statistics.

I suck at Calculus. Hard. Like, I would be failing that class if our teacher didn't give such ridiculous grading curves all the time, and a 50-point project that is basically extra credit. That said, calculus is supposedly easier when you take it again (or so people tell me), so maybe I'll get it in college. Then again, maybe not. Actually, probably not at all. I think I'm going to be a chemical engineer (chemistry was actually one of my good classes), so knowing which parts of Calculus I'll actually need to use would be beneficial, too.
Hell, to the trained eye it looks like gibberish, too. I think it's because our teacher teaches it a completely different way, though. I'm totally getting a 1 on the exam. No questions asked.

When you take college-level chemistry, you'll find out.

My chemistry teacher started doing a derivative while explaining a formula, etc. The derivative was done strangely though, as he did: sin(x) -> -cos(x) -> sin(x) :in that order. Except I sin(x) doesn't derive into -cos(x). Oh well!

I know there's more but we haven't deeply integrated chemistry and calculus (no pun intended) in my class.

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Sredni Vashtar

#14 April 08, 2008, 12:22:26 pm

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Um, I have never ever taken an intro to chemistry course before that has needed calculus in any way. Not even algebra.

But then again they were intro level classes. When I take Engineering Materials this summer it's basically the same thing as chemistry and I bet I'll need calculus though!

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mar77a

#15 April 08, 2008, 02:31:06 pm

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Quote from: Omcifer on April 07, 2008, 10:00:34 pm

∫{0..1} (x-1)/(x+1) dx
Split into two integrals:
= ∫{0..1} x/(x+1) dx - ∫{0..1} 1/(x+1) dx

First integral:
∫{0..1} x/(x+1) dx
Let u = x+1 → du = dx and x = u-1
= ∫{x=0..1} (u-1)/u du
= ∫{x=0..1} 1 - 1/u du
Split into two integrals:
= ∫{x=0..1} 1 du - ∫{x=0..1} 1/u du
= u - ln|u| {x=0..1}
= (x + 1) - ln(x + 1) {x = 0..1}
= [(1 + 1) - ln(1 + 1)] - [(0 + 1) - ln(0 + 1)]
= 2 - ln(2) - 1 + 0
= 1 - ln(2)

Second integral:
∫{0..1} 1/(x+1) dx
Let u = x + 1 → du = dx
= ∫{x=0..1} 1/u du
= ln|u| {x=0..1}
= ln|x + 1| {x=0..1}
= ln|1 + 1| - ln|0 + 1|
= ln(2) - ln(1)
= ln(2)

Combining the two integrals:
= [1 - ln(2)] - ln(2)
= 1 - 2ln(2)
= 1 - ln(2^2)
= 1 - ln(4)

That should be right, if not then it can't be too far off!

Barrow, ca ching!

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BlackRaven

#16 April 08, 2008, 02:42:57 pm

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This is pretty basic stuff. We did things like this in the first math course I had in college. Five math courses so far (still first year), but I'm studying to become a physicist so that's...

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goldenratio

#17 April 08, 2008, 03:14:50 pm

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Hey Velfarre I'm a programmer and I never use calculus. The only time you'd use it is if you were game programming, and even then usually only for physics type stuff. The basics of derivation/integration should be enough to do most of the stuff you will ever do in programming (so like one class' worth?).

yes coulombs are "germaine", did you learn that word at talk like a dick school?

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Mateui

#18 April 08, 2008, 07:30:41 pm

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For anyone taking Calculus and struggling, I HIGHLY recommend "Calculus For Dummies". That book saved my life in University and got me an A in both my semesters of taking it (and I never took Calc. in high school. That's how good the book is).

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Fire Mage

#19 April 09, 2008, 12:20:27 am

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You know Omcifer, your solution was really dragged out. I realized the easiest solution: use Long Division.

(x+1) into (x-1) = 1 with a remainder of -2, so you "convert" that to -2/(x+1)

Then:

Code:[Select]

∫ (1 + (-2/(x+1)) dx
= ∫dx - ∫ 2/(x+1) dx
= 1 - 2∫ 1/(x+1) dx
= 1 - 2Ln(x+1)
= 1 - Ln(x+1)^2

Then you proceed to substitute in; so yeah Long Division is a lot faster. Haha.

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Lars

#20 April 09, 2008, 12:48:17 am

Fuck off!
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Quote from: Mateui on April 08, 2008, 07:30:41 pm

For anyone taking Calculus and struggling, I HIGHLY recommend "Calculus For Dummies".

I took your word for it and just ordered Calculus for Dummies and Physics for Dummies. This'd better be worth it!

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