Effin' integrals.

[eLiu]

Nooooooooooooooooooooooooooo!!..

Why TecHNooB, why?

I tried to dangle the carrot just a little lower. To see if the 10 yr old gi... rabbit would stand up and bite. It's like with the original problem, she had to jump up. After your hint, she had to jump a little.

With TecHNooB's hint, we're practically stuffing the carrot (well, not the same carrot; this is part 2 after all!) in the bunny's mouth. But she won't open up to receive our gift.


OP: Now that you know the solution to part 1, can you fill in "?" and "??" in my earlier posts? Can you prove why?

Furthermore, what kind of retard school do you go to? Seriously?! What the fuck kind of shitbrained "math major" cannot solve these problems???

These are so basic. They hardly require any knowledge of calculus. They require you to take 1 or 2 (max) simple properties and apply them in the most direct possible way. Somehow this is asking too much.

This is what's wrong with America's "higher" education system. There's nothing "higher" about it. All these fuckwits going to school, getting a fancy piece of paper, and thinking they're smart, have knowledge, and are worth more than my shit. Then they try to find a job and are so confused when people realize they're incapable of independent, logical thought.

Though to be honest, I really thought part 1 was harder than part 2. I'm dumbfounded to see that someone could solve part 1 but not part 2.

OP again:
"Integrating dz=k*x^(k-1)dx is not really going to get me anywhere. It just proves l(x^k)=l(x^k)... which is useless if I need to prove kl(x) = l(x^k)."
Wha... wai.. wha... I... wha?? ????
????
At one point, I thought this thread was hilarious. Now it mostly makes me want to cry.
OP, they give you an incredibly awkward definition of l(x) = int( dx/x, x=1..x). If I asked for l(2), what would the definition be? int( d2/2,2=1..2)?! What about l(y)? In the original definition, what's the integrand? What are the bounds? Are those x's the same?!?!
OK you "figured" that out. WRITE DOWN the integral definition of l(x^k). PLUG IN z = x^k. HOW ARE YOU NOT DONE?!


edit: and let me be clear. When and if you solve this problem or any of these problems, there will be NO moment of brilliance. DO NOT be proud of yourself. You have accomplished nothing.

edit2: At some level I guess you can't blame TridenT for the stupidity of his TAs. Given his knowledge of calculus and the "rest of his class", I have the sickening feeling that his TAs were once in his shoes. They were spoonfed by those that came before them. And so the cycle of anti-learning continues, with each generation at least as stupid as the one before it.

 

[TridenT]

god you're such a whiner. when you go to the tutoring center, and they do the problems and show you. you ASK them questions to understand what's going on. take the initiative yourself to learn this stuff and understand it fully, stop fucking making excuses.

It's not like I could understand the guy anyway, he is from another country. (Some country in south-east Asia)

 

[MovingTarget]

It's not like I could understand the guy anyway, he is from another country. (Some country in south-east Asia)

Could you not at least read his handwriting? If he did indeed work it out for you, he likely didn't do that purely by speaking. Half of my math department spoke fluent RUSSIAN, yet I was able to understand their English quite well (even when the accents were heavy). This isn't some humanities course you are talking about here....this is MATH. It is the easiest to learn when you understand the speaker the least.

Edit: Let me restate that last sentence. Suppose you are going to another country to university. You struggle with the language. The subject you would have the least trouble with should be math. This has been a common thing that I have heard from foreign exchange students in the US.

 

[eLiu]

Could you not at least read his handwriting? If he did indeed work it out for you, he likely didn't do that purely by speaking. Half of my math department spoke fluent RUSSIAN, yet I was able to understand their English quite well (even when the accents were heavy). This isn't some humanities course you are talking about here....this is MATH. It is the easiest to learn when you understand the speaker the least.

His TAs are either as dumb as he is (see above post about spoonfeeding) OR they, like me, are so confused about what he's confused about... that they don't know what to do.

And in their home countries, with this level of dumb, you'd never make it to college. Or high school. Or anything. They're probably sitting there wondering if TridenT & his brethren are a sign of the apocalypse.

I ran into this issue as an (undergrad) TA often--I could not understand what my students did not understand. But at least I was getting paid there, so I was happy to sit down and try and explain how linked lists work 20 different ways.

 

[busydude]

Edit: Let me restate that last sentence. Suppose you are going to another country to university. You struggle with the language. The subject you would have the least trouble with should be math. This has been a common thing that I have heard from foreign exchange students in the US.

I am an international student.. and math was by far the easiest.. I mean it virtually made no difference, we already know the terminology.. and 90% of math lectures is made up of them.

 

[TridenT]

Yeah... so, I get as far as k*int(dx/x, 1...x^k) and then I realize... "x^k in thing... fuck. How fix, what do..."

EDIT: Yeah, I don't know if the x's are the same or if they're different. (I think they might be different because he likes to do that) My professor is very ambiguous.

I've been trying the route that they're the same. Maybe they're different.

 

[eLiu]

Yeah... so, I get as far as k*int(dx/x, 1...x^k) and then I realize... "x^k in thing... fuck. How fix, what do..."

EDIT: Yeah, I don't know if the x's are the same or if they're different. (I think they might be different because he likes to do that) My professor is very ambiguous.

How did you get here: k*int(dx/x, 1...x^k)?

"Yeah, I don't know if the x's are the same or if they're different"
^^What do you think?

It is a little confusing notation. The book or your prof or whoever is using one variable where there are usually two. Which x's have to do with the integrand? Which x's have to do with the bounds of integration? This is *extremely* fundamental. If you do not understand this, there's no point to proceeding with this problem. If you do understand this, you should see what to do.

The integrand and the bounds for integration are always 2 separate entities. Rewrite the problem. Give them different names. Then look at that hint, and think about whether the "x" in z=x^k refers to the integrand or the bounds, and why.

 

[TridenT]

How did you get here: k*int(dx/x, 1...x^k)?

"Yeah, I don't know if the x's are the same or if they're different"
^^What do you think?

It is a little confusing notation. The book or your prof or whoever is using one variable where there are usually two. Which x's have to do with the integrand? Which x's have to do with the bounds of integration? This is *extremely* fundamental. If you do not understand this, there's no point to proceeding with this problem. If you do understand this, you should see what to do.

The integrand and the bounds for integration are always 2 separate entities. Rewrite the problem. Give them different names. Then look at that hint, and think about whether the "x" in z=x^k refers to the integrand or the bounds, and why.

 

[eLiu]

LOL dude. Before even starting on part 2, your solution for part 1 is COMPLETELY wrong. You don't fully understand the difference btwn the integrand and the bounds of integration. But you have identified the difference on the first line of part 1.

I can guarantee you that the full solution to part 1 needs the 'hint' I gave you earlier.

The trouble with part 1 is that you haven't really stated anything. The first line is the definition of l(x) and a restatement of the hint. The second line is more of the same. The third line states what you want to prove. The fourth line made me LOL hard.

Edit: part 2 is wrong as well, but vaguely (coincidentally?) on the right track. The first line restates the definition & Hacp's hint.
Why is your definition of l(x) written different here than in part 1?
The second line demonstrates that you don't understand what l(x) really means. So if I asked you to write down l(2), you would tell me: integral of d2/2 from 1..x

That is what you're telling me when you say that l(z) = integral of dz/z from 1..x. (Unless I'm misreading your handwriting?)

edit2: to further prove my point, let's say that I tell you that the anti-derivative of 1/z is ln(z). Then using a certain theorem of calculus that I have referenced before, you should be able to evaluate your expression on line 2 of your part 2 explicitly. What do you get?

 

[TridenT]

LOL dude. Before even starting on part 2, your solution for part 1 is COMPLETELY wrong. You don't understand the difference btwn the integrand and the bounds of integration.

I can guarantee you that the full solution to part 1 needs the 'hint' I gave you earlier.

That's the same solution I was given by the asian kid.

I just went with it.

 

[eLiu]

That's the same solution I was given by the asian kid.

I just went with it.

I've already established that your TA is a bloody fucking idiot. The fact that he can't tell left from right doesn't mean you need to follow blindly. THINK BOY, THINK.

 

[TridenT]

LOL dude. Before even starting on part 2, your solution for part 1 is COMPLETELY wrong. You don't fully understand the difference btwn the integrand and the bounds of integration. But you have identified the difference on the first line of part 1.

I can guarantee you that the full solution to part 1 needs the 'hint' I gave you earlier.

The trouble with part 1 is that you haven't really stated anything. The first line is the definition of l(x) and a restatement of the hint. The second line is more of the same. The third line states what you want to prove. The fourth line made me LOL hard.

Edit: part 2 is wrong as well, but vaguely (coincidentally?) on the right track. The first line restates the definition & Hacp's hint.
Why is your definition of l(x) written different here than in part 1?
The second line demonstrates that you don't understand what l(x) really means. So if I asked you to write down l(2), you would tell me: integral of d2/2 from 1..x

That is what you're telling me when you say that l(z) = integral of dz/z from 1..x. (Unless I'm misreading your handwriting?)

edit2: to further prove my point, let's say that I tell you that the anti-derivative of 1/z is ln(z). Then using a certain theorem of calculus that I have referenced before, you should be able to evaluate your expression on line 2 of your part 2 explicitly. What do you get?

Idk. What I have looks about right to me. Shit, even what the asian kid wrote looks correct.

 

[eLiu]

Idk. What I have looks about right to me. Shit, even what the asian kid wrote looks correct.

lolgasm, I fail. I thought you wrote int(dt/t, t=1..x) + int(dt/t, t=1..xy). Yeah then that's correct.

You should justify why int(dt/t, t=1..x) + int(dt/t, t=x..xy) is true. One way is to use that theorem of calculus I keep referencing. This is exactly the question I asked you earlier, except some terms will simplify out since some of the variables "a,b,c,d" turned out to be the same.

edit: and for the love of god write int( dt/t, t=1..xy). d(xy)/xy, (xy) = 1.. xy just looks so... dirty.

 

[Hacp]

You can't really do it that way easily because you'd need to change both the upper and lower limits when substituting x^K for Z. There is an easier way to do it and I'll give you a hint. It is the only equation in the HINTS section that you haven't written down yet.

Edit:Just to clarify, for the method you have on your sheet, for the lower bound, you'd have to say z=1 so 1=x^k and 0=x . But x=0 is not your target for the lower bound.Your target is x=1. So you'll need to add and subtract terms to get it in a form that will look like the given identity. Who knows, there might be a simple way of manipulating it so everything works out but it will take time.

 

[TridenT]

You can't really do it that way easily because you'd need to change both the upper and lower limits when substituting x^K for Z. There is an easier way to do it and I'll give you a hint. It is the only equation in the HINTS section that you haven't written down yet.

Edit:Just to clarify, for the method you have on your sheet, for the lower bound, you'd have to say z=1 so 1=x^k and 0=x . But x=0 is not your target for the lower bound.Your target is x=1. So you'll need to add and subtract terms to get it in a form that will look like the given identity. Who knows, there might be a simple way of manipulating it so everything works out but it will take time.

This is what I have. I thought the [1,X] didn't matter and was a different variable entirely. I don't really get it.

 

[Dr. Zaus]

This is what I have. I thought the [1,X] didn't matter and was a different variable entirely. I don't really get it.

http://www.khanacademy.org/#Calculus

 

[TridenT]

http://www.khanacademy.org/#Calculus

Not helping unless you cite specific video. :\

 

[eLiu]

Not helping unless you cite specific video. :\

Ok, consider the integral of f(x)dx, from a..b

I tell you that the antiderivative of f(x) is F(x). that is, dF/dx = f(x)

Write that integral in terms of F(x). What theorem did you just apply?


Now, you wrote l(z) = integral of 1/z *dz, from 1..x
I tell you that the antiderivative (or really the problem tells you) of is 1/z is ln(z). Write the integral in terms of ln(z). Call whatever you end up with "Y".

You have defined z = x^k. So you have l(z) = l(x^k) = ln(x^k) = Y

Does something stand out to you as being fishy?
While you cannot prove part 2 using the properties of logs, you can at least double-check your existing steps. Tragically this "technique" is useless in most proofs, but luckily you already know the answer here.

once again, THINK BOY, THINK.

The [1,x] bounds for integration DOES matter. When I say I'm going to integrate f(t)dt from x to y, what does that mean? I assume you learned the definition of the integral through the Riemann sum... look back at that. Explain to me in words what that definition means. The letters x,y,t, etc. represent something. It's not just a matter of "oh I see an 3 'x' marks on the page, they must all be the same thing."

is the integral of f(x)dx from 1..x the same as the integral of f(t)dt from 1..x the same as the integral of f(t)dx from 1..x the same as the integral of f(x)dt from 1..x? Your answer use the theorem referenced above (the one I keep referring to) and other simple properties of integrals. I give you that dF/dx = f(x) and dF/dt = f(t) as before. Write down what all these integrals are in terms of f(t), f(x), F(x), and F(t) as appropriate.

Why is it that you have written:
l(x) = integral f(x)dx from 1..x
and
l(x) = integral f(t)dt from 1..x

everything here comes back to the same fucking issue. If you don't understand the difference btwn the limits of integration and the integrand, then how are the previous two integrals equivalent? One uses t and teh otehr uses x! CLEARLY DIFFERENT, RIGHT? (Hint: Starts with an N, ends with the only repeated letter in FRUIT LOOPS.)

 

[A Casual Fitz]

It saddens me that so many Trident threads get so many replies.

 

[TridenT]

Shiiit. I figured this might happen guys! PEOPLE FROM MY MATH CLASS KNOW ME ON ATOT NOW because they all been googling this problem. D:

One guy even registered and even PM'd me. He's in the same class as I am. Lol.

 

[busydude]

Shiiit. I figured this might happen guys! PEOPLE FROM MY MATH CLASS KNOW ME ON ATOT NOW because they all been googling this problem. One guy even registered and even PM'd me. He's in the same class as I am. Lol.

Hahahahaha!!.. I needed a laugh after a boring day.. thanks. Now get a life.

 

[Matthiasa]

lol
Well as long as they don't find your photos you might be safe.
However when your professor or ta finds it you might get screwed.

 

[MovingTarget]

Shiiit. I figured this might happen guys! PEOPLE FROM MY MATH CLASS KNOW ME ON ATOT NOW because they all been googling this problem. D:

One guy even registered and even PM'd me. He's in the same class as I am. Lol.

Tell them to post here. Perhaps we can better understand the situation with another viewpoint.

Google, like a TI-89, can become too much of a crutch in calculus. Beware.

 

[MovingTarget]

lol
Well as long as they don't find your photos you might be safe.
However when your professor or ta finds it you might get screwed.

He might guess what is up when he goes into class and everyone is munching on fruitloops. Lulz.

:whiste:

 

[TridenT]

lol
Well as long as they don't find your photos you might be safe.
However when your professor or ta finds it you might get screwed.

There's no TA, and I doubt the professor really searches for solutions online when he makes them.