Thread: Left end points

Consider the given function.
Evaluate the Riemann sum for 2 ≤ x ≤ 14, with six subintervals, taking the sample points to be left endpoints.

Part 1 of 3

We must calculate L₆ =

6	f(xi−1) Δx = [f(x0) + f(x1) + f(x2) + f(x3) + f(x4) + f(x5)] Δx,where x0, x1, x2, x3, x4, x5 represent the left hand endpoints of six equal sub-intervals of [2, 14]
i=1

Since we wish to estimate the area over the interval [2, 14]
using 6 rectangles of equal widths, then each rectangle will have width Δx=2



We wish to find L₆ = (2)[ f(x₀) + f(x₁) + f(x₂) + f(x₃) + f(x₄) + f(x₅)].
Since x₀, x₁, x₂, x₃, x₄, x₅
represent the left-hand endpoints of the six sub-intervals of [2, 14],
then we must have the following.

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I know that delta x= 14-2/6 which is 2. I'm not sure how to get these values:

x0,x1,x2,x3,x4,x5. Do I have to make the graph?

I appreciate any advice or insight!!

Hey Steelers72.

Hint: x0 = 2, x1 = 2 + deltax = 4, x2 = 2 + 2*deltax = 6, and so on.... (Now just evaluate the functions at these points)

Thanks ! If you don't mind, how exactly did you get the values? Like, which formula or equation did you start to plug numbers in?

Your questions asks for equal-sub intervals which means the space between them is constant and happens to be the delta x value.

OH now I remember when did this in lecture. when they dont give you a graph you take the x axis value and multiply it by the delta x. thanks again!!!