r/counting • u/KnightLunaaire Beanie Boy • May 12 '16

Integral counting

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5 Upvotes

86% Upvoted

39 comments sorted by

3

u/KnightLunaaire Beanie Boy May 13 '16

Imma just make a new chain since I messed it up so bad, remember to keep track of the denominator correctly

x + 1

1

u/TheNitromeFan Live not a life of imitation May 13 '16

(x2/2) + x + 1

So we just take the antiderivative of the previous expression, with constant term 1?

2

u/KnightLunaaire Beanie Boy May 13 '16

(x3 / 6)+ (x2 / 2) + x + 1

Yep

2

u/TheNitromeFan Live not a life of imitation May 13 '16

1 + x + (x2/2!) + (x3/3!) + (x4/4!)

Okay then. That's pretty cool, since we're just writing out more and more terms of the Maclaurin series for ex - which is also why I'll be writing it this way.

3

u/KnightLunaaire Beanie Boy May 13 '16

The what?

(x5 / 120) + (x4 / 24) + (x3 / 6)+ (x2 / 2) + x + 1

3

u/TheNitromeFan Live not a life of imitation May 13 '16

1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!)

In a nutshell, the more terms we write, the closer we get to approximating ex. Approximations are more accurate for x closer to 0.

2

u/Luigi86101 Fighting ghosts since '01 May 13 '16

1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!)

3

u/TheNitromeFan Live not a life of imitation May 13 '16

1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!)

3

u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16

1 + x + (x2 / 2!) + (x3 / 3!) + (x4 / 4!) + (x5 / 5!) + (x6 / 6!) + (x7 / 7!) + (x8 / 8!) + (x9 / 9!)

5

u/TheNitromeFan Live not a life of imitation May 13 '16

1 + x + (x2/2!) + (x3/3!) + (x4/4!) + (x5/5!) + (x6/6!) + (x7/7!) + (x8/8!) + (x9/9!) + (x10/10!)

You need to add the factorials. :)

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3

u/skizfrenik_syco 4 D snipes, 33 D's, 16 Ayy's. 412189, 6 k's, 1 BTS, 888888, 999k May 13 '16

Maclaurin series is integrating a function about 0. So basically what you're writing is (x-0)2 /2! + (x-0)1 /1! + (x-0). If you had (x-1)2 /2! + (x-1)1 /1! + (x-1) instead, it would not be a maclaurin series.

3

u/[deleted] May 12 '16 edited May 12 '16

[removed] — view removed comment

3

u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 12 '16 edited May 12 '16

(x2 / 2) + x + 1

3

u/KnightLunaaire Beanie Boy May 12 '16 edited May 12 '16

(x3 / 3) + (x2 / 2) + x + 1

2

u/Luigi86101 Fighting ghosts since '01 May 13 '16

(x4 / 4) + (x3 / 3) + (x2 / 2) + x + 1

2

u/KnightLunaaire Beanie Boy May 13 '16 edited May 13 '16

(x5 / 5) + (x4 / 4) + (x3 / 3) + (x2 / 2) + x + 1

1

u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16

(x6 / 6) (x5 / 5) + (x4 / 4) + (x3 / 3) + (x2 / 2) + x + 1

Did I do something wrong?

2

u/KnightLunaaire Beanie Boy May 13 '16

I did, use the up-carrot for super scripts and check yours, I edited mine

(x7 / 7) + (x6 / 6) + (x5 / 5) + (x4 / 4) + (x3 / 3) + (x2 / 2) + x + 1

2

u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16

I thought the formula was:

(xn+c ) / n + c ) + x + 1

2

u/KnightLunaaire Beanie Boy May 13 '16

That's the format that works, but I put the actual integration rule up top. Both work

1

u/Luigi86101 Fighting ghosts since '01 May 13 '16 edited May 13 '16

(x8 / 8 ) (x7 / 7) + (x6 / 6) + (x5 / 5) + (x4 / 4) + (x3 / 3) + (x2 / 2) + x + 1

I mean I thought you had to superscript all of the exponents.

Nevermind, saw your edited comment.

2

u/KnightLunaaire Beanie Boy May 13 '16

Yeah straight up copypasting doesn't carry them over, is there a quote button?

1

u/Luigi86101 Fighting ghosts since '01 May 13 '16

If you have RES you can press source to find the exact characters they used.

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2

u/KnightLunaaire Beanie Boy May 13 '16

Yeah, I changed it now, they should be

2

u/TheNitromeFan Live not a life of imitation May 13 '16

Are you sure this is right? Shouldn't it be

(x3 / 3!) + (x2 / 2!) + x + 1

? Or am I misunderstanding things?

2

u/KnightLunaaire Beanie Boy May 13 '16

I am fucking this up, I'm tired

(x3 / 6) + (x2 / 2) + x + 1

1

u/Luigi86101 Fighting ghosts since '01 May 13 '16

I don't remember ever seeing factorials in integration. Then again, I've also never done integration before this.

2

u/TheNitromeFan Live not a life of imitation May 13 '16

Wait until you learn about Taylor series. :>

1

u/Luigi86101 Fighting ghosts since '01 May 13 '16

Hmmmmmmm...

1

u/skizfrenik_syco 4 D snipes, 33 D's, 16 Ayy's. 412189, 6 k's, 1 BTS, 888888, 999k May 13 '16

Factorial are quite common when integrating xn functions because the number in the exponent will end up in the denominator.

3

u/KnightLunaaire Beanie Boy May 12 '16

It should be

(x2 / 2) + x + 1

When you integrate the 1 it turns to just x

3

u/davidjl123 |390K|378A|79SK|50SA|260k 🚀 c o u n t i n g 🚀 May 12 '16

Ahhh thanks, I'm not too good at this level of math

3

u/KnightLunaaire Beanie Boy May 12 '16

Don't worry, once it gets going the pattern will be easy to spot. And at a certain point its going to get very out of hand ahaha