Problem

1. $[2 / 3$ Points] DETAILS PREVIOUS ANSWERS SCALC9 4.2.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the Riemann sum for $f(x)=2 x-1,-6 \leq x \leq 4$, with five equal subintervals, taking the sample points to be right endpoints.

Solution

Step 1 :Given a function \(f(x) = 2x - 1\), an interval \([-6, 4]\), and a positive integer 5, the Riemann sum can be calculated by dividing the interval into 5 equal subintervals, and summing up the areas of the rectangles formed by the function values at the sample points and the widths of the subintervals.

Step 2 :The width of each subinterval is \((b - a) / n = (4 - (-6)) / 5 = 2\).

Step 3 :The right endpoints of the subintervals are \(-6 + 2 = -4\), \(-4 + 2 = -2\), \(-2 + 2 = 0\), \(0 + 2 = 2\), and \(2 + 2 = 4\).

Step 4 :The Riemann sum is then the sum of the function values at these points times the width of the subintervals.

Step 5 :The Riemann sum for the function \(f(x) = 2x - 1\) over the interval \([-6, 4]\) with five equal subintervals, taking the sample points to be right endpoints, is -10.0.

Step 6 :Final Answer: \(\boxed{-10.0}\)

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