flat assembler
Message board for the users of flat assembler.
Index
> Heap > Sum of a Finite Series 
Author 

MHajduk
Your formula is improper mainly because you have forgotten integrated function symbol and you've "lost" somewhere limes on the right side of the equation.
This should be more accurate: Integral (in the simple words) is a limit of the sums of series for the n → ∞ 

27 Sep 2010, 07:54 

Tyler
I'm new to calculus, and learning it independently. I wrongly thought that the "f(x)dx" was the formula to find the solution. What is "dx" anyway? Some call it a differential, is that the same as a derivative? As for the limits, it originally had "delta X > 0". In theory, it adds the infinite rectangles in the integral, with f(n delta x) being the height, and delta x being the width.


27 Sep 2010, 22:01 

MHajduk
Tyler wrote: What is "dx" anyway? Some call it a differential, is that the same as a derivative? And yes, concepts of the differentials and derivatives are related: sometimes derivatives of the functions are denoted as a quotients of the differentials. More detailed explanations of what I wrote above you may find here: 

28 Sep 2010, 08:39 

Tyler
So they are essentially the same thing? The real integral equation is just height, or f(x), times width, or the [infinitesimally small] change in x?
What would be the differential of x be, in the context of an xy graph? Doesn't it change constantly? 

02 Oct 2010, 21:01 

MHajduk
I'm not sure what are you asking about actually, but I'll try to answer anyway.
Basically, definite integral of the function f (f: R → R, where R is a set of the real numbers) with the low limit a and high limit b is interpreted usually as a area under curve f(x) (exactly sum of the areas under the curve f(x) and over the x axis [for the parts where f(x) ≥ 0] and areas under the x axis and over the f(x) curve taken with minus sign [for the parts of the chart where f(x) < 0]) between the points x=a and x=b. Equation written by me in the one of the previous posts shows how we can calculate approximations of the integral value. With the n getting bigger (consequently Δx getting smaller) approximation is getting better. k is a number of the vertical strip under the f(x) curve (from x=a+kΔx to x=a+(k+1)Δx), f(a + kΔx) is a height of this strip, Δx is a width of the each of the strips (here, for simplicity, we assumed that all strips have the same width). 

02 Oct 2010, 22:39 

< Last Thread  Next Thread > 
Forum Rules:

Copyright © 19992020, Tomasz Grysztar. Also on YouTube, Twitter.
Website powered by rwasa.