like in n sigma i=1 (Xi)changeX. what does X subscript i stand for? or what does it mean?
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Summation of each "iteration" (i) of x.
For example, let's say we're adding rectangles, starting at x = 1, to x = 5, x_1 = 1, x _2 = 2, x_3 = 3, etc. "i" represents each individual iteration. It's a way of not having to list each of these x-values. Intsead we start with the "first number" (i = 1), "add all the values" (Sigma), "up to 10" (the number at the top of the sigma symbol n = 10, or whatever may be there.".
Hope that helps!
For example, let's say we're adding rectangles, starting at x = 1, to x = 5, x_1 = 1, x _2 = 2, x_3 = 3, etc. "i" represents each individual iteration. It's a way of not having to list each of these x-values. Intsead we start with the "first number" (i = 1), "add all the values" (Sigma), "up to 10" (the number at the top of the sigma symbol n = 10, or whatever may be there.".
Hope that helps!
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∫[a,b] f(x) dx := lim[n->∞] ∑{i=1,n} f(t_i) Δx_i
...................^ defined as
The whole key is the underlying need for a partition of the interval [a,b]. A partition is a set
P = {a = x₀, x₁, ..., x_n = b} such that a = x₀ ≤ x₁ ≤ x₂ ≤ ... ≤ x_n = b. So the sum is being taken over every subinterval of the partition [x₀,x₁], [x₁,x₂], etc. t_i is any point in the subinterval [x_{i-1},x_i] and Δx_i := x_i - x_{i-1}.
That's about all the detail I can go into here. Search around if you want more detail on the definition of the Riemann Integral.
...................^ defined as
The whole key is the underlying need for a partition of the interval [a,b]. A partition is a set
P = {a = x₀, x₁, ..., x_n = b} such that a = x₀ ≤ x₁ ≤ x₂ ≤ ... ≤ x_n = b. So the sum is being taken over every subinterval of the partition [x₀,x₁], [x₁,x₂], etc. t_i is any point in the subinterval [x_{i-1},x_i] and Δx_i := x_i - x_{i-1}.
That's about all the detail I can go into here. Search around if you want more detail on the definition of the Riemann Integral.