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.
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Particular integral is finding what the integral is for example the integral of 2x is x^2 + C. Finding the particular solution would be finding what C equals from the particular integral.
3 Sigma is 66800 defects per million pieces 6 Sigma is 3-4 defects per million pieces You can check out the number of defective pieces per million & the % accuracy for all Sigma levels in the six sigma conversion chart in the related links section
In simple language, derivative is rate of change of something and integral represents the area of a curve whose equation is known.
Sigma Mu Sigma was definitely at Lynchburg College between 1968-1972.