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On another sketch, represent the right Riemann sum with approximating ∫. Write out the terms of the sum, but do not evaluate it.

a) f(c₁)Δx + f(c₂)Δx + ... + f(cₙ)Δx
b) f(c₁)Δx - f(c₂)Δx - ... - f(cₙ)Δx
c) f(c₁) + f(c₂) + ... + f(cₙ)
d) f(c₁) - f(c₂) - ... - f(cₙ)

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Final answer:

The right Riemann sum to approximate the integral of a function is represented as the sum of the products of the function values. The correct answer is a).

Step-by-step explanation:

The correct representation for the right Riemann sum for approximating the integral is option a) f(c₁)Δx + f(c₂)Δx + ... + f(cₙ)Δx. This sum corresponds to the calculated area of the rectangles placed over the curve of the integrand f(x) from x₁ to x₂, with the right ends of the rectangles touching f(x).

In this method, the use of Δx (delta x) represents the width of each rectangle and f(cᵢ) is the function evaluated at the right endpoint of each subinterval on the x-axis. Therefore, the right Riemann sum is the sum of the areas of these rectangles and gives an approximation for the integral of f(x) over the interval [x₁, x₂].

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