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Summation, represented by sigma (Σ) is the discreet version of integration.
Integration is the continuous version of summation.
It can be somewhat hard to explain the difference between discreet and continuous phenomena.
The best way to think about integration is as the area under a line, curve, or function. Think of a triangle formed by lines y=0, x=1,and y=x. written mathematically, this is the integral x=0 to 1 of (x). You can also calculate the area of a half unit circle. integral x=-1 to 1 of (sqrt(1-x^2)).
The best way to think about summation is the adding of numbers. sum x=0 to 1 of (x) yields the equation (0+1). sum x=-1 to 1 of (sqrt(1-x^2)) yields the equation (0+1+0).
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What is the difference between Integration and differentiation?
integration is reverse of differentiation and vice versa
What does summation of infinite series?
The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.
What is the difference between integrity and integration?
Interrogation is where you force someone to tell you and integrate is totally the opposite
What is the difference between integration and derivation?
Integration results in an equation which gives the area under the original equation between the bounds. Derivation results in an equation which gives the slope of the original line at any point.
What is the difference between sigma and integral?
Sigma is a discrete sum, a sum with steps. Eg. add the numbers from 1 to 10 or add the numbers 1/2, 1/4,... A sigma always has a concept of a next thing to add, even if the list of things goes on forever. An integral is a continuous summation. It is a summation in that we are adding up the area under the curve, for example, but it is continuous in that because we are adding things of arbitrary smallness it's not really possible to always point to the individual terms that are being added because they become some kind of continuous blur. Instead we use some mathematical technique (integration). But still it is a kind of summation.
