Reimann Sum Setup

**petenice** · November 30th 2012, 07:13 AM

Im having trouble setting up this Reimann Sum. The question is
Find the Riemann sum for f(x) = sin(x) over the interval [0, 2π],

where x₀ = 0, x₁ = π/4, x₂ = π/3, x₃ = π, and x₄ = 2π, and

where c₁ = π/6, c₂ = π/3, c₃ = 2π/3, and c₄ = 3π/2. (Round your answer to three decimal places.)

So heres what i understand. n = 4, so there are 4 rectangles of uneven size. x₀ - x₄ are the given intervals.

I m guessing i should take $\sum_{i=1}^{n}$ $f(c_i)\Delta{x_i}$ and set it up like this $\sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}$ .

But thats where im stuck. Do i evaluate each right end point times $\Delta{x_i}$ and add them up? Does $\Delta{x_i}$ = $\frac{2\pi}{n}i$ or $\frac{2\pi}{4}i$

Any help is greatly appreciated.