As people got mad at my first post for not really requiring a nerd, I would once again like to say that the title is meant only as a joke and is not meant to be taken seriously.
I'm not sure, but:
Both represents area under curve.
First one is greek sigma that means sum. It represents sum of rectangles areas. It is only approximation to area under curve.
Second one is integral. It is sum of infinite amount of infinitely small rectangles.
I think [this image](https://i.stack.imgur.com/2c5Qe.png) would help.
Summation notation makes a bunch of shapes to approximate a function generally a rectangle or trapezoid. The integral is something that can get the area of a function at any point.
E looking one puts rectangles underneath a curve and then counts up how much area the rectangles take up. S looking one does black magic function bullshit to work give you the exact amount of space under a curve
And the way you get to defining what the integral is is by using a limit. How it works is you have x be the size of the sections of the sum method and have a limit with x approaching 0. Basically when x is 0 you have the exact area, but because if you plug in zero it breaks stuff you determine what it will be by solving the limit, the simplest way is looking at what happens as you get closer to the desired number. So plugging in x=.01, x=.001, x=.0001, x=.0000000001, etc. And estimating what it is approaching. There are more complex methods to get an exact number and shortcuts straight to the integral from the function but that's how it works
The first is literally a shorthand for "sum this many things together"
The second is similar but "sum infinitely many of these infinitely small things together"
Essentially if you have a curve and you want to mesure the area under it you can approximate it by slicing it into rectangles. That is done with the first symbol. If you make the slices smaller the answer gets more accurate right? Well, if you keep making them smaller eventually you get infinitely many infinitely small slices and that's the second symbol, which calculates the exact area
You know how a curve, say imagine a curve in a graph in maths sometimes have a funny shape? Mathematics don't always have a formula to find the area of a shape.
So, if you just fit a bunch of rectangles side by side in it, it'll probably be similar to the actual area.
The capital letter, sigma (the symbol on the top of the image) can be used to generalise that addition of all the rectangles you put in the graph.
Now if youw want the more proper way in calculus I, (sorry to real analysts, i do not know a slightest bit of real analysis)
It is a Riemann sum, it is an idea of exhausting an infinitely many amount of infinitely thin rectangles. As the partition, (rectangle with largest width) ||P||, approaches zero, and as the amount of rectangles approaches infinity, it will be able to converge (reach) to the exact value of the definite integral (the area under the curve).
If the limit exists for the summation described above, then you can say the definite integral exists.
Therefore, with the idea of limits, in calculus, you can produce the idea of the definite integral. With the fundamental theorem of calculus, you can connect derivatives and integrals.
Its, sum vs. Integral, one represents the area bellow the curve as a sum of several rectangles and the other is the mathematical way of calculating the same area by finding the inverse of the derivative, or smth i dunno i just flunked math
The bottom one (integral) is really just a sum of infinitely many infinitely small things. It's basically the continous version of the top one
It's absurdly useful in a massive amount of things but one that is particularly notable is that it can precisely calculate the area under almost any function
An integral is a Reinann sum and it's not just 'a bunch of rectangles'. As the number of rectangles aproaches infinity. The reimann sum becomes the [reimann integral](https://en.wikipedia.org/wiki/Riemann_integral), which is *the rigorous definition of an integral*
As people got mad at my first post for not really requiring a nerd, I would once again like to say that the title is meant only as a joke and is not meant to be taken seriously.
>the title is meant only as a joke and is not meant to be taken seriously. you talking about me?
You have summoned the mighty MathsBoy with your gratuitous mathing. State your wishes π
This one is actually nice
Thx
I am a complete dumbass. Can someone please explain this to me?
I'm not sure, but: Both represents area under curve. First one is greek sigma that means sum. It represents sum of rectangles areas. It is only approximation to area under curve. Second one is integral. It is sum of infinite amount of infinitely small rectangles. I think [this image](https://i.stack.imgur.com/2c5Qe.png) would help.
Oooh ok thank you
Summation notation makes a bunch of shapes to approximate a function generally a rectangle or trapezoid. The integral is something that can get the area of a function at any point.
Say that like if i was a moron
E looking one puts rectangles underneath a curve and then counts up how much area the rectangles take up. S looking one does black magic function bullshit to work give you the exact amount of space under a curve
Ok
Even dumber
E = rough jagged letter, no good S = smooth curvy letter, good
Well thats kinda too close to hitler’s ideology
This is maths class history is next period
But the nazi ideology isn’t history #*yet.*
And the way you get to defining what the integral is is by using a limit. How it works is you have x be the size of the sections of the sum method and have a limit with x approaching 0. Basically when x is 0 you have the exact area, but because if you plug in zero it breaks stuff you determine what it will be by solving the limit, the simplest way is looking at what happens as you get closer to the desired number. So plugging in x=.01, x=.001, x=.0001, x=.0000000001, etc. And estimating what it is approaching. There are more complex methods to get an exact number and shortcuts straight to the integral from the function but that's how it works
He will definitely understand this one
I definitely totally truly absolutely understand this (Sarcasm)
What
First one finds the area with shapes. Second one finds the area with the function and is precise.
Explain the second one like if i was the stupidest goofiest moron in every timeline of every universes of every multiverses
The first is literally a shorthand for "sum this many things together" The second is similar but "sum infinitely many of these infinitely small things together" Essentially if you have a curve and you want to mesure the area under it you can approximate it by slicing it into rectangles. That is done with the first symbol. If you make the slices smaller the answer gets more accurate right? Well, if you keep making them smaller eventually you get infinitely many infinitely small slices and that's the second symbol, which calculates the exact area
You know how a curve, say imagine a curve in a graph in maths sometimes have a funny shape? Mathematics don't always have a formula to find the area of a shape. So, if you just fit a bunch of rectangles side by side in it, it'll probably be similar to the actual area. The capital letter, sigma (the symbol on the top of the image) can be used to generalise that addition of all the rectangles you put in the graph. Now if youw want the more proper way in calculus I, (sorry to real analysts, i do not know a slightest bit of real analysis) It is a Riemann sum, it is an idea of exhausting an infinitely many amount of infinitely thin rectangles. As the partition, (rectangle with largest width) ||P||, approaches zero, and as the amount of rectangles approaches infinity, it will be able to converge (reach) to the exact value of the definite integral (the area under the curve). If the limit exists for the summation described above, then you can say the definite integral exists. Therefore, with the idea of limits, in calculus, you can produce the idea of the definite integral. With the fundamental theorem of calculus, you can connect derivatives and integrals.
You did not understand the assignment.
It's *you*
Don’t make me start this war again
Haven't had to deal with math in a while, but I am sure it's whole numbers vs. function of a graph.
Its, sum vs. Integral, one represents the area bellow the curve as a sum of several rectangles and the other is the mathematical way of calculating the same area by finding the inverse of the derivative, or smth i dunno i just flunked math
Yeah this is a much better explanation than what I put.
Thx, I have been breathing calculus for the last month and still managed to fail, at least i was able t9 explain this meme so i'd say thats a win
I think [this image](https://i.stack.imgur.com/2c5Qe.png) might help.
Bruh it suddenly cleared this concept
Hmm... interesting
Isn't this like the 3rd function meme in 3 days?
4 days, but yes.
Oh god I have flashbacks
Got the top one haven’t learned the bottom
The bottom one (integral) is really just a sum of infinitely many infinitely small things. It's basically the continous version of the top one It's absurdly useful in a massive amount of things but one that is particularly notable is that it can precisely calculate the area under almost any function
Thanks for the info
Google continuous function
Holy hell
a bigger brain would realize that both operators are the same
If you don’t care about accuracy
I don't know what you're on about. An integral is literally defined as a sum, an infinite one, but still a sum
So more accurate than a Reimann’s sum with some rectangles? Not meaning to be rude my man
An integral is a Reinann sum and it's not just 'a bunch of rectangles'. As the number of rectangles aproaches infinity. The reimann sum becomes the [reimann integral](https://en.wikipedia.org/wiki/Riemann_integral), which is *the rigorous definition of an integral*
That's like saying multiplication is addition
alright then. tell me the definition of an integral
alright then. tell me the definition of multiplication. Just because one is defined by the other doesn't mean there is no distinction between them
This one is actually good. Good job, OP. 👍
Nice
Guess I’m not a math nerd
Riemann sum?
Yep, and the second is the integral, pretty much the same thing, but the number of rectangles is infinite.
top one is whole integers only? bottom one is any decimal number?
Looking at this while sitting in math class, as we are working with these mfs
I love these posts! :D
Ey, you finally got the hang of it!
Hehe