A sine integral by Riemann sums Consider the integral I =
Chapter 5, Problem 63(choose chapter or problem)
A sine integral by Riemann sums Consider the integral I = 1 p>2 0 sin x dx. a. Write the left Riemann sum for I with n subintervals. b. Show that lim uS0 ua cos u + sin u - 1 211 - cos u2 b = 1. c. It is a fact that a n - 1 k = 0 sin apk 2n b = cos a p 2n b + sin a p 2n b - 1 2a1 - cos a p 2n b b . Use this fact and part (b) to evaluate I by taking the limit of the Riemann sum as nS _.
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