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 calculateL_{6}=

6 f(x_{i−1}) Δx= [f(x_{0}) +f(x_{1}) +f(x_{2}) +f(x_{3}) +f(x_{4}) +f(x_{5})] 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 findL_{6}= (2)[f(x_{0}) +f(x_{1}) +f(x_{2}) +f(x_{3}) +f(x_{4}) +f(x_{5})].

Sincex_{0},x_{1},x_{2},x_{3},x_{4},x_{5}

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!!