/sci/ - Science & Math

It's correct, you're a fucking retard. DING DING DING!

>>10978391
What the derivative or RHS? What is the definition of antiderivative?

>>10978400
mean

>>10978391
what is your argument

C just changes by 1/2

>>10978391
ur dumb

>>10978400
I am under the assumption that substitution is not the correct method for finding the antiderivative when integrating a polynomial to the first degree. Pic related is my argument for the antiderivative.

>>10978424
this explains nothing to me

>>10978431
that's the same shit, dude
c doesn't matter

dude let x-1 = t

dt = dx

int (x-1) dx = int t dt = t^2/2 = (x-1)^2/2

QED

>>10978391
>>10978431
+C you fucking retard

>>10978424
[math]
\dfrac{(x-1)^2}{2} \\
=\frac{1}{2}\left ( x^2 -2x+1\right ) \\
=\frac{1}{2}x^2-x+\frac{1}{2}
[/math]
Optimized.

yikes

>>10978391
whats the ''right '' solution op?

>>10978391
brainlet kys

>>10978451
yikes goes in all fields, OP leave this board immediately

>>10978431
>He can't wrap his head around C
IQ thread is around the corner anon

faggot

>>10978391
Call me a retard as 4chan may, but wouldn't the answer be (x^2)/2 - x + C ?

>>10978499
This is my argument.

>>10978391
I understand that C is an arbitrary constant. If i needed to find a particular solution with the general solution that he provided, which is what we were doing in class, I would be off by 1/2.

>>10978499
that's the same (up to a constant)

>>10978442
>optimized

>>10978431
you and your teacher are both retarded. it makes no difference

>>10978400
>>10978424
>>10978434
>>10978440
>>10978441
>>10978442
>>10978451
>>10978460
>>10978461
>>10978469
>>10978486
>>10978537

>>10978506
Explain this. Like I said, I understand that C is an arbitrary constant, and can, and should, be combined with 1/2 and still be C. Not combining it with C leaves a term of 1/2 in the general solution. This, to my knowledge, is incorrect. Any work, like finding a particular solution at a given point, would be incorrect, and off by 1/2.

>>10978506
No, you wouldn't be off by 1/2. It will always cancel out when you take a definite integral.

>>10978562
In any definite integral you take F(b) - F(a), in which case all constants (including the half) cancel out.

>>10978566
>>10978573

ok, i see that. it will not cancel out in a particular solution.

>>10978562
i bet your teacher already explained it but you didn't listen. it makes no difference

>>10978577
It still won't matter. If you're given a condition like F(0) = 0, your C will simply be 1/2 + the professor's C, and you will end up with the exact same equation.

>>10978583
Cont.
And by the way, substitution always works as a method to solve integrals. It's just the integral formulation of the chain rule.

>>10978562
same shit, the only thing that changes is the height, so they're the same except for the c

>>10978578
I explained my understanding of it in the post that you quoted.

My argument is that all constants should be included in the constant of integration.

>>10978594
this shows what happens when they're not

>>10978604
It doesn't make a difference, even when finding a particular solution. Try applying a condition like F(0)=0 and see what happens.

>>10978604
only the shape matters dude

>>10978607

>>10978607

When you integrate a function, you don't get ONE function, but a SET of function.
Be the constant C or C + 1/2, the generated set of function is fundamentally the same.

>>10978632
You're so close! Now just plug the value for C back into each equation to find the particular solution. And expand your professor's version so it becomes more clear.

>>10978644
Did OP realize what a retard he is?

>>10978562
>Any work, like finding a particular solution at a given point, would be incorrect, and off by 1/2.
Every value of C is a solution, it doesn't make sense for it to be off by 1/2, because just changing by 1/2 is still a solution.

>>10978680
I think he was assuming the C in his equation and the C in his professors equation had to be equal. One (autistic) way to avoid this is to use subscript numbers like [math]C_n[/math] until you decide to combine constants at the end of whatever work you're doing - then drop the subscript or swap to some other letter or whatever.

>>10978562
>This, to my knowledge, is incorrect
well it's not

>Any work, like finding a particular solution at a given point, would be incorrect, and off by 1/2.
what? no it wouldn't
can you give an example of this?

>>10978691
>I think he was assuming the C in his equation and the C in his professors equation had to be equal.
If he actually thought that he is LITERALLY retarded.

>>10978695
I know we're supposed to be mean here, but it's a really common baby mistake. OP's probably pretty young.

>these are the people who argue with the professor and brag about it on /sci/
just fucking lol

>>10978699
It's not that he made a mistake. It's that he argued with his professor because he was so absolutely sure he was smarter than them when he made such a retarded mistake.

>>10978717
Fair. Hopefully the shame teaches him not to be such a faggot. If that lesson can sink in, he might still make it.

>>10978732
lol nah these types never stop being this way unless they drop out

>>10978746
Come on, I'm willing to believe in him.

>>10978391
An arbitrary constant plus a constant is another arbitrary constant. So your teacher is right.

>>10978391
The only thing worse than a pedantic autist is a pedantic autist who's wrong. Jesus fucking christ, you know that you're literally the type of student that everyone (including the professor) wishes wasn't in their class, right?

>>10978391
>Am I justified in my argument?
No lmao you are just incredibly confident in your misunderstanding

>>10978717
I made the same mistake and i argued with my professor but i wanted him to make things clear for me not ro prove him wrong.
And some other times i did prove my teachers wrong

>>10978604
>My argument is that all constants should be included in the constant of integration.
good luck defining this for an arbitrary function and not just polynomial

stfu retard cant even do basic calculus but trying to argue with your teacher about something you're wrong about. maybe put faith in him when you have no clue what you're talking about since you're too dumb to understand his explanation.

>>10978391
This is how they learn integrals in Europe. That way the students don't assume that the integral is a linear operator before they've taken linear algebra. It's the superior way to do it.

>>10978877
>prove my teachers wrong
>I'm not wrong EVERY time, so I'll go right ahead and remain an overconfident, argumentative faggot

Your whole attitude is backwards.

>>10978391
It must be hard to be a brainlet. You're teacher is right and you should stop sucking so many cocks, OP.

$$R^2 = 1 − \frac{SSE}{SST} = 1 − \frac{Var(e)}{Var(y)},$$

>>10978391
>56 replies

Bait thread. You can't be this autistic.

>>10978562
thats why they give initial conditions in de
you solve for C

>>10979777
linear algebra doesn't explain why integral is a linear operator. it just gives you the definition.

>>10978847
wait a minute...

>>10978391
snapped and going into my /sci/ humor compilation

>>10978391
The antiderivative only exists as a set of functions. There's 'a' antiderivative, but not 'the' antiderivative.
When you compute the integral with Newton's theorem (i.e. you compute F(b) - F(a), the real reason anyone actually cares about the so-called indefinite integrals) the additive constant disappears.
d/dx isn't an injective map from C^1 to C, so any antiderivative is only unique up to being summed with an element of the kernel.
Try reading an actually worthwhile Calculus book.

>>10980745
The point is to make the integral less intuitive, as it should be to beginner calculus students. It builds good habits in mathematicians, and filters students in other areas of STEM. It's not much, but seeing as how all lower division math is geared towards non-mathematicians, it's necessary.

>>10979777
definite integral is a linear map (linear functional) froms continous functions subspace in the interval [a.b] to R. But what about anterivation, what is this?

>>10978431
it doesn't matter, since C can be anything

>>10978442
thanks for posting anon

>>10978391
Plug any integer into c and find the derivative, you'll get x -1

>>10982235
This may also work if you plug in half of an integer.

>>10978406
Statistics is that way

>>10978562
It doesn't matter at all, it's correct either way.
Many would consider your "teacher's" answer to be cleaner and more informative than yours.

>>10982448
would this be true if the number was +324234983045350503945934509304540303953049 ?