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flyingpig
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Homework Statement
The formal definition of the integral is
[tex]\lim_{n \to \infty} \sum_{i=1}^{n} f(x_i)\Delta x[/tex]
The Attempt at a Solution
My question is, why does i = 1? Why don't we start at i = 0?
flyingpig said:Homework Statement
The formal definition of the integral is
[tex]\lim_{n \to \infty} \sum_{i=1}^{n} f(x_i)\Delta x[/tex]
The Attempt at a Solution
My question is, why does i = 1? Why don't we start at i = 0?
flyingpig said:If it is too much to ask, can you draw me a picture...?
An integral is a mathematical concept that represents the area under a curve in a graph. It is used to calculate the total amount or quantity of something.
An integral is calculated by finding the antiderivative of a function and evaluating it at the upper and lower limits of integration. This is often done using integration techniques such as substitution, integration by parts, or trigonometric substitution.
A definite integral has specific limits of integration and gives a numerical value as the result. An indefinite integral has no limits and gives a function as the result.
The constant of integration is a constant term that is added to the result of an indefinite integral. It is necessary because when finding the derivative of a function, the constant term will disappear. The constant of integration allows us to account for all possible solutions.
The integral is used in various fields such as physics, engineering, economics, and statistics. It can be used to calculate the area under a velocity-time graph to determine the distance traveled, or to find the total cost of producing a certain number of items. It is also used in probability and statistics to calculate the probability of an event occurring.