Let's see who on /sci/ is actually good at the ultimate form of mathematics, integration.
>>7664932
I'm not, have done very little work with it, and it was all over the MAT this year, which fucked me because all my prep was in algebra, geometry, trig and functions/derivatives
>analytic integration
no thanks
>>7664932
Math you can do by typing it into a calculator is boring.
>>7664932
0.333333
The proof is trivial
The ultimate form of math!
>>7664964
> 0.333333/
> meaning 333333 / 1000000
> not 1/3
> meaning you used a calculator
> and pretended that you solved it
> but also failed to realize that 1/3 does not have a finite decimal expansion
i wish i could even understand what that means :\
>>7664976
>being autistic
>>7664977
It means "find the area under a curve of a function that is completely irrelevant and OP is only using it as an example because he spent way too much time solving a problem that a calculator can do and wants other people to waste their time, too."
i'm in S (the scinetific physic and math section at my college[France])
and i do not understand what this equation is
Can someone explain? (I'm basicaly the equivalent of a sophomore)
>>7664964
i.e. "i just put that shit in Wolfram"
>>7664976
Like I give a fuck. This is a shit thread, and I wanted to post the "trivial proof" maymay
stop being a fucking autist for one day
>>7664977
Well you know that the real numbers are, right. So consider polynomials whose coefficients are make it so you can just subtract any multiple of x^2 + 1. The resulting space R[x] / (1+x^2) is known as the complex numbers, and we usually write x = i. Every complex number can be written uniquely as a + bi with a,b real.
We then write e^z = [math]\sum_{k=0}^\infinity z^k / k![/math]. If we write [math]e^(i z)[/math] as a+bi with a and b real, then a is the cosine, b is the sine, and a/b is the tangent.
Now suppose f is a continuous function, and we have an interval [a,b]. Divide a,b into smaller intervals [math] [x_i, x_i+1] [/math], take the maximum and minimum points of f in each subinterval, call the max on each interval U_i the min on each interval V_i and add U = sum of [math]U_i (x_{i+1} - x_{i})[/math], V = sum of [math]V_i (x_{i+1} - x_{i})[/math] It can be shown that we can choose partitions to make the absolute value of U - V arbitrarily small. So as the partition size gets smaller U and V tend to the same limit, which is called the integral from a to b of f.
So let f(x) = 1/(sqrt(sin(x)) + sqrt(cos(x)))^4 and calculate its integral.
>>7664963
I can do mathematical proofs by typing it into my programmable calculator.
Given a statement in 1st order arithmetic, It is decidable whether a number is an encoding of a proof of a theorem. So I program my HP calculator to tell me whether each number is a proof of the theorem I want, and then just have it check the every natural number in order until I get a proof of the theorem I want. You don't even need a HP 48 or TI graphics calculator one of the older programmable HP calculators works just as well.
>>7665004
that has been in no way simplified.
>Ultimate form of mathematics
>Integration
>>7665035
It is literally the definition of all the terms in the problem.
>>7665036
>being new
idk yet but I'll be learning power series soon and then I'll be able to do it
>being a physicist
First year student here, we started integration two weeks ago, its ok. Not really ultimate.
>>7665067
A minute to learn, a lifetime to master. Like reversi. Or Go.
>>7664932
u = tan(x), du = [math]\sec^2(x)[/math]
Answer = 1/3
>>7665191
>using tex for part of your answer
>dropping a dx
You are one of the worst posters ive seen here
>>7665067
You're not really allowed to give an opinion on integration until you get to measure theory
For what practical reason would you solve this shit?
>>7665261
They teach measure theory to engineers in ETH Zurich, which is vastly superiour to all schools in the Anglosphere with the possible exception of Cambridge and Princeton.
>>7665274
Ok?
>>7664967
tfw...
>>7665543
forgot the ^4 lol oops
>>7664932
>implying the ultimate form of mathematics isn't higher dimensional topology
>>7665029
>inductions can solve all proofs
>brute force will solve all proofs
Lol dumbass
>>7665776
>>7665776
My calculator program always finds the shortest proof in Peano Arithmetic for any theorem in Peano Arithmetic. Of course I can reprogram it to brute force search for proofs in other axiom schemes like ZFC. Yes, doing such a brute force will take an extremely long time to prove even the most trivial theorem, but the original claim was that "math you can do by typing it into a calculator is boring" and I provided a way to prove any mathematical theorem that is deducible from the given axioms by typing it into a calculator. Of course there are some theorems that are true but not provable from the axioms, but most mathematicians use ZFC almost exclusively anyway.
>>7664932
No, fuck that.
I won't even use the step by step in mathematica to do that
Not in the mood to do homework you put over a color gradient
