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Math 2413 Homework 4.3 Riemann Sums & Definite Integrals
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.
Sketch the figure, showing each xi’s and ci’s. Identify the norm ∆ . ___________
Find the Riemann sum for f(x) = sin x over the interval [0, 2π] such that there are 4 regular partitions and ci’s are the
midpoints of each partition.
Sketch the figure, showing each xi’s and ci’s. Identify the norm ∆ . ___________
Write the area of the region determined by f(x) = sin x over the interval [0, 2π] as a definite integral. Find its value.