Question

Find the Riemann sum for

Answer 1

Mathematically speaking, the Riemann sum of the linear function is represented by A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}, whose representation is represent by the graph in the lower left corner of the picture.

What figure represents a Riemann sum with right endpoints?

Graphically speaking, Riemann sums with right endpoints represent a sum of rectangular areas with equal width with excess area for positive y-values and truncated area for negative y-values generated with respect to the x-axis. Mathematically speaking, this case of Riemann sums is described by the following expression:

A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, ..., n}

Where:

a - Lower limit

b - Upper limit

n - Number of rectangles

i - Index of a rectangle

If we know that f(x) = 2 · x - 1, a = - 6, b = 4 and n = 5, then the Riemann sum with right endpoints of the area below the curve is:

A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}

To learn more on Riemann sums: brainly.com/question/21847158

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