Effin' integrals.

[masteryoda34]

solve for the points where 1 + x^2 = 1 + x

 

[Hacp]

Step 1: Draw the first curve
Step 2: Draw the 2nd curve
Step 3: If all the points in the 2nd curve are above the 1st curve, then the 2nd integral>first integral. Vice versa if its the other way around.

If you can't figure this simple stuff out, you are doomed. Period. Quit school and look for a job at Mcdonalds.

 

[MovingTarget]

Definitely going to have to visit the tutoring center on Tuesday... this guy has assigned only 10 problems (one of which was something that I could do) but the rest are like "wtf..."

He is the worst math teacher I've ever had. He doesn't teach. He hasn't talked about any of this shit in class.

Are you taught by a TA or actual professor. He may in fact post here if it is the former. That would be funny.

 

[busydude]

Are you taught by a TA or actual professor.

I am a TA myself. Thank god that Trident is not my student.

 

[MovingTarget]

I am a TA myself. Thank god that Trident is not my student.

I was a TA, but I graduated with my masters. TridenT is probably better in person, but one thing I would not put up with as a TA were people who wanted me to do their work for them (i.e. be too forthcoming in my help). I'd still help him though, but he would have to meet me halfway and put the effort in.

 

[paulney]

Effing integrals, how do they work?!!!

 

[TridenT]

Are you taught by a TA or actual professor. He may in fact post here if it is the former. That would be funny.

Professor. He's horribly bad. Lack of good teachers in America... :thumbsdown:

 

[artikk]

NOOOOOOOOoOOOoooooOO you gave it away

edit: though mad propz to anyone who can work out hte integral on the left by hand. I guessed (=bullshitted) the solution... it's really similar to integrating ln(x), something I assumed after integrating by parts. In this case, it helps to know that derivative of asinh(x) = 1/sqrt(1+x^2). It comes out to 1/2(x*sqrt(1+x^2) - asinh(x)). Not sure how that would've helped the OP even if he could derive it, lol.

Can't you just use a trig substitution and that will be equal to some trig function squared which will be simplified by the square root. Of course, the limits will need to be adjusted accordingly. I'm not sure about the properties of integrals hint though. Been a year or so since I took any kind of math class.
ex 1+ x^2=1 + cot(theta)^2
x=cot(theta)
csc(theta)^2=1 + cot(theta)^2
integral of ( csc(theta) dtheta), 0 to 1
Any analogous(in form) trig identity will do.

 

[Born2bwire]

Definitely going to have to visit the tutoring center on Tuesday... this guy has assigned only 10 problems (one of which was something that I could do) but the rest are like "wtf..."

He is the worst math teacher I've ever had. He doesn't teach. He hasn't talked about any of this shit in class.

Yes yes, whine whine whine.

eLiu is correct, this is completely trivial. All you need to do is understand what an integral does.

Effing integrals, how do they work?!!!

Haha. I was going to post this too. :awe:

 

[MovingTarget]

Professor. He's horribly bad. Lack of good teachers in America... :thumbsdown:

Good teachers are ones that care whether or not their students 'get it'. There are plenty of good teachers, but not enough jobs available for them. The flooded corporate market for PhD's and Graduate level researchers is another contributor, as lack of jobs there causes them to retreat to academia.

Have you actually talked with your professor? Does he know YOUR name? These can make all the difference.

 

[TridenT]

Good teachers are ones that care whether or not their students 'get it'. There are plenty of good teachers, but not enough jobs available for them. The flooded corporate market for PhD's and Graduate level researchers is another contributor, as lack of jobs there causes them to retreat to academia.

Have you actually talked with your professor? Does he know YOUR name? These can make all the difference.

This guy is most definitely not that then. He does not ask once during a whole 2+ hour lecture/rant/ramble/fond-memories-of-his-education-in-Germany(I think Germany it was) whether we are getting anything. People will rarely speak up and say, "Uh. I don't get it." "What don't you get?! It's simple, you see? Yeah, simple. What isn't there to get?"

And we're all there like, "Uh... No, that. I don't get that." And we'll try to explain and he just rambles more and gets us to the point where we're so frustrated from trying to get him to explain things clearly that we just give up and pray instead.

We only have him two days a week but for 2:20 hours per class meeting. And we don't have school on many Monday's or Wednesdays this term so it's becoming even more difficult.

Blah. The man is old and has a thick Italian or German accent. He doesn't do examples or problems or anything. He just pretty much does proofs and theorems on the board which are OK if you get it... or are explaining it well, but he fails at that miserably.

I have talked to him once to get an idea of what is going to be on the tests, but he's so vague... he says he'll give us an idea or practice tests/exams or study guides or something. I can't recall, but he's definitely putting the screws in on us with the way he teaches.

 

[busydude]

I'm not sure about the properties of integrals hint though.

If f(x)<=g(x) and the limits of integration are the same for both functions, then:

integral(f(x))<=integral(g(x))

That is exactly what Hacp suggested in post 27.

 

[coxmaster]

Professor. He's horribly bad. Lack of good teachers in America... :thumbsdown:

Weird.. My university has TONS of awesome professors. In fact I think ive only had 1 bad professor.

I guess quality of the school does matter

 

[TridenT]

Not like I am goin' to ask for help anymore anyway, but here is what we have to do by Wednesday. All of us who are in the class that haven't taken Calc II recently are not getting it at all. (There's some in the class who took Calc II equivalents already)

http://img204.imageshack.us/img204/825/32344330.jpg 50(did that), 52
http://img404.imageshack.us/img404/3497/31374438.jpg 65, 66
http://img51.imageshack.us/img51/7840/63146119.jpg 54, 58, 60
http://img441.imageshack.us/img441/9038/62075673.jpg 12 (I got that done easily)
http://img708.imageshack.us/img708/4002/17172886.jpg 48 (Not too sure)
http://img191.imageshack.us/img191/984/14660777.jpg >_<

 

[TridenT]

Weird.. My university has TONS of awesome professors. In fact I think ive only had 1 bad professor.

I guess quality of the school does matter

It probably also depends on how much money your school has.

I had probably one of the best math teachers ever for my Calc I class last term at another CC... She was like a goddess compared to this math Nazi.

I already took Calc I and Calc II in high school but that was three years ago or so... So I don't remember anything and this guy is surely making anything that I could remember all fucked up.

 

[artikk]

If f(x)<=g(x) and the limits of integration are the same for both functions, then:

integral(f(x))<=integral(g(x))

That is exactly what Hacp suggested in post 27.

Oh I get it. Thanks for the explanation. This is easier to picture visually though.

 

[busydude]

Not like I am goin' to ask for help anymore anyway, but here is what we have to do by Wednesday.

Don't tell me you can't solve question 50.

Edit: ninja'd

 

[TridenT]

Don't tell me you can't solve question 50.

Edit: ninja'd

Psh. It wasn't true ninja because it shows the "edited at suchandsuch"

 

[MovingTarget]

This guy is most definitely not that then. He does not ask once during a whole 2+ hour lecture/rant/ramble/fond-memories-of-his-education-in-Germany(I think Germany it was) whether we are getting anything. People will rarely speak up and say, "Uh. I don't get it." "What don't you get?! It's simple, you see? Yeah, simple. What isn't there to get?"

And we're all there like, "Uh... No, that. I don't get that." And we'll try to explain and he just rambles more and gets us to the point where we're so frustrated from trying to get him to explain things clearly that we just give up and pray instead.

We only have him two days a week but for 2:20 hours per class meeting. And we don't have school on many Monday's or Wednesdays this term so it's becoming even more difficult.

Blah. The man is old and has a thick Italian or German accent. He doesn't do examples or problems or anything. He just pretty much does proofs and theorems on the board which are OK if you get it... or are explaining it well, but he fails at that miserably.

I have talked to him once to get an idea of what is going to be on the tests, but he's so vague... he says he'll give us an idea or practice tests/exams or study guides or something. I can't recall, but he's definitely putting the screws in on us with the way he teaches.

Unfortunately it isn't going to get any better in terms of theorems vs. specific examples. You have to go through the proofs step by step and prove them yourself. If he is spending his time doing this in class instead of specific examples, then it is doable.

Aside from that, does he have regular office hours posted? Classtime doesn't count as far as asking questions. He is there to present the material and only has two days per week to do it. If the class is large, then the opportunity for questions during that time should be slim.

You can do this, TridenT. It will be a pain in the butt, but it is doable. Read the book, take better notes, go through his proofs with a fine-tooth comb, show the professor know you have done this, and then ask him, "how can I come up with and evaluate a specific example of this theorem in action?" This is the last step.

 

[eLiu]

If f(x)<=g(x) and the limits of integration are the same for both functions, then:

integral(f(x))<=integral(g(x))

That is exactly what Hacp suggested in post 27.

you guys... taking all the fun out of this thread D:

also, artikk, substituting x=cot(u) will not work trivially.

You'd have the int(csc(u) dx). Note the dx. dx = -csc^2(u)du. Good luck integrating -csc^3(u)du.

Something similar resutls with my first attempt, which was x=tan(u). Then you get stuck integrating sec^3(u)du. Whoo... that's a lot better right? >< And that's when I started trying to "use the force" instead of math.


Also OP, having an awesome or shitty math teacher doesn't really matter for solving problems like this. There's so little substance here. One function is less than (or equal to) the other one; this is true at every point. The integral is the "area under the curve"... so if one curve is always below its friend... durrr.

There's not a ton to teach. If you don't like how teh prof explains things, go find some more books from the library. Find a friend who understands the material. Look online; there are tons of video lectures and such. But most of all, use your brain. I highly doubt you're going to find any material anywhere that step-by-step explains how to do this exact problem or even something similar to it.

edit: and finally, some akshual advice. When at first you don't succeed, plot it. Trying to find a limit? Plot it. Comparing integrals? plot it. Proving that a specific function has a particular property? Plot it. Having that physical picture in front of you is often helpful to understand what's going on. I can say with certainty that you don't know what sqrt(1+x^2) and sqrt(1+x) actually look like. Calculus gets hard when "plot it" isn't an option anymore.

 

[Hacp]

Not like I am goin' to ask for help anymore anyway, but here is what we have to do by Wednesday. All of us who are in the class that haven't taken Calc II recently are not getting it at all. (There's some in the class who took Calc II equivalents already)

http://img204.imageshack.us/img204/825/32344330.jpg 50(did that), 52
http://img404.imageshack.us/img404/3497/31374438.jpg 65, 66
http://img51.imageshack.us/img51/7840/63146119.jpg 54, 58, 60
http://img441.imageshack.us/img441/9038/62075673.jpg 12 (I got that done easily)
http://img708.imageshack.us/img708/4002/17172886.jpg 48 (Not too sure)
http://img191.imageshack.us/img191/984/14660777.jpg >_<

The last one is easy not because it is easy but because they fucking give you the answer in the hint. Hint: READ THE HINT!!!!!!!!!

Dear Trident, I suggest you major in something easier like basket-weaving or Afro-American Studies.

 

[TridenT]

The last one is easy not because it is easy but because they fucking give you the answer in the hint. Hint: READ THE HINT!!!!!!!!!

Dear Trident, I suggest you major in something easier like basket-weaving or Afro-American Studies.

I read the hint. It doesn't make much sense if you're not already very fluent in Calc stuff. :|

I'm good at doing the regular types of problems, not these ones that are based more off the language.

 

[busydude]

I read the hint.

The hint is the answer!! If you are having hard time understanding the hint.. then how will you be able to solve it?

 

[TridenT]

The hint is the answer!! If you are having hard time understanding the hint.. then how will you be able to solve it?

Exactly... did you read past that first sentence?

 

[busydude]

Exactly... did you read past that first sentence?

What do you mean by regular type of problems? My point is, if you can't understand the hint.. its better you not solve the problem.

I have to ask, do you know the concept of additivity of integral?