@hentaispyder  
That sound awesome, aw

This entire thread broke my brain.

Dat flank

@Background Pony #B61D  
Um I don’t think pony wings have a brain or mental disability. Maybe they look wrong I dunno, it looks fine to me.

@Background Pony #B61D  
Not sure if pony hate, or just bad articulation of a general dislike of the wing style.

@mathprofbrony @Raiinbow Dash @Background Pony #A211  
Don’t use your fancy mathematics to muddle the issue!
 
(Enumerated the eggheads for you, @Princess♠Molestia)

“I love integrals.”
 
<eye twitch>
 
INTEGRALS
 
I HATE INTEGRALS

@this thread
 

 
…
 
cries inwardly at own insecurities

I’m REALLY expecting people reading the mug as “I love Dicks.”  
Was very disappointed.

@Background Pony #A211  
Yes, he is referencing the integration of the Gaussian bell-curve.

@mathprofbrony  
Gaussian integral, correct? Also, note I limited my statement to elementary functions for a reason: when you get all un-elementary all hell breaks loose in a good way.

@mathprofbrony  
I wouldn’t say the integration is easier if the indefinite integration is completely impossible. I’m not sure that this would actually apply to this argument. Nevertheless, it is a cute integral.
 
Also funny how the number pi likes to pop up in all sorts of calculations. I always thought that was weird. Just like e, except pi is cooler than e because reasons.

@mathprofbrony
 
*definite
 
Traditionally math proofs end with a Q.E.D. But hey, it’s summer, and you guys are cool.

Wow, you guys got a lot further into the math than I would have. But! I have a beautiful example of a definite integral that is easier to do than an indefinite integral. I do it in my calc classes.
 
e^(-x^{2).
 
This is the bell curve. Now, as an indefinite integral, you can’t integrate this at all. Its integral is “the error function,” which you can only approximate with series or such. But we do know that its indefinite integral from -infinity to infinity is the square root of pi.
 
How?
 
Look at it like this. Square your integral.
 
(int e}(-x^{2) dx) (int e}(-x^{2) dx).
 
Change the variable in the second: that change doesn’t change the value. Call it y.
 
(int e}-x^{2 dx) (int e}-y^{2 dy).
 
Now you can bring those two together and make it a double integral over the xy-plane:
 
int int e}(-x^2-y2) dx dy.
 
Here’s the trick. Convert to polar coordinates. The area differential dx dy becomes r dr dtheta. And -x^2-y2 becomes -r^{2, because r}2 = x^{2 + y}2. The bounds become 0 to 2pi in theta and 0 to infinity in r. Your integral becomes
 
int int e^(-r^{2) r dr dtheta
 
Change order and the theta integral first: there’s no theta in the integrand, so it’s just a constant as far as theta is concerned. You get theta e}(-r^{2) r, evaluated from theta=0 to theta=2pi. So you get
 
int 2pi r}(-r^{2) r dr = 2pi int r e}(-r^{2) dr
 
And you can do this integral! Use u-substitution: u=-r}2, du = -2r dr. The integral becomes
 
2pi int e^{u (-1/2) du = -pi int e}u du
 
So the value is ~~pi e^u, evaluated from 0 to infinity. That becomes -pi (0 ~~ 1) = pi.
 
So the square of your integral is pi.
 
So the original integral is sqrt(pi).
 

I had to search for an old book to understand this again.

@Raiinbow Dash  
Somewhere around the point that you claimed x^3*ex is odd. But regardless, I see no point in going further with the discussion, the claim most odd functions have a definite integral of 0 is something I can grant (not all, for there’s plenty with holes and asymptotes).

@Raiinbow Dash  
I meant to say “odd function times an even function”. *cough*

@Background Pony #A211  
Maybe we got off somewhere, but I wasn’t trying to compare the two separate operations. I was stating that a definite integral involving an odd function with limits equidistant from zero should be, and is, easier to calculate than the indefinite integral of the same function.
 
Here is an example that will hopefully clarify:
 
*int( x^3 cos(x) dx ): (indefinite)
 
This calculation requires integration by parts. This calculation requires multiple steps.
 

 
int( x^3 *cos(x) dx ) from -pi to pi: (definite)
 
This is the same integral. It can be noted, however, that this function is odd. Since this function is odd (this should be intuitive, because it is an odd function times an odd function) and the limits are equidistant from zero, that the value of this integral will come to 0.  
——  
That being said, these are the kind of examples I was referring to, apologies for any misunderstandings.
 
If this still doesn’t make sense, then I’m afraid I don’t understand your argument.

And that’s why I switched from engineering to accounting. Because math up to calculus is fun and happy, and math afterwards makes me sad.

@Raiinbow Dash  
And I’m responding that your argument for it not being the case is flawed because you are comparing two inherently different things and making arguments about their relative difficulty. What’s harder, discrete analysis or algebraic number theory? Combinatorial topology or algebraic topology?

@Background Pony #A211  
I believe you are thinking too hard about this. I was only pointing out that “indefinite integrals are easier than definite integrals because you are missing a step” is not necessarily true in every case. While it may be said that in most cases this is true, it is not true for every case.
 
 
@Applejack  
Me too! I got out of calc 4 a couple semesters ago, and I’m kinda glad it’s over myself lol.

>tfw I’m done with math for the rest of my life
 

 
I liked sequences and matrices though.

@Raiinbow Dash  
While you could argue that finding the definite integral of x^{3 is easier than finding it’s indefinite integral (x}4/4), I don’t find the use of x^{3 * e}x dx to be conductive to anything as they are, in fact, completely different operations. You wouldn’t have any easier time finding the definite integral by intuition with that one than you would trying to find the indefinite integral by intuition. It’s like saying the farmer’s walk is harder than crossfit, is mepoint. It’s too condition dependent and doesn’t really yield a natural way to compare difficulty because both activities are just too different.

@Lupin Quill  
“New” is subjective. I have been here about a year and a half. I am newer than some but not as new as others.