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funcosed
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Homework Statement
Could someone define the notion of an integral for a map,
x → g(x), x element of R2
or
xn+1=g(xn
thanks
funcosed said:Homework Statement
Could someone define the notion of an integral for a map,
x → g(x), x element of R2
or
xn+1=g(xn
thanks
An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value or quantity of a function over a specific interval.
The purpose of defining an integral for a map x → g(x) is to find the total value or quantity of the function g(x) over a specific interval. This allows us to calculate important information about the function, such as the average value or total change.
The integral for a map x → g(x) is defined as the limit of a sum of infinitely many rectangles, each with a width of Δx, as Δx approaches zero. This is expressed mathematically as ∫g(x)dx = limΔx→0 Σg(x)Δx.
A definite integral for a map x → g(x) has specific boundaries or limits of integration, while an indefinite integral does not. The definite integral gives a numerical value, while the indefinite integral gives a general function or family of functions.
Defining an integral for a map x → g(x) has many applications in real-world problems, such as finding the area under a velocity-time graph to determine distance traveled, calculating the work done by a variable force, and finding the average value of a function over a given interval.