each interval has width π/4
so, the sum is just
R6 = π/4 (sin(π/4) + sin(2π/4) + sin(3π/4) + sin(4π/4) + sin(5π/4) + sin(6π/4))
= π/4 (1/√2 + 1 + 1/√2 + 0 - 1/√2 - 1)
= π/4 * 1/√2
repeat for M6, but use the midpoints k * π/8, k = 1,3,5,7,9,11
(a) Find the Riemann sum for f(x) = 2 sin(x), 0 ≤ x ≤ 3𝜋/2, with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.)
R_6 = ?
(b) Repeat part (a) with midpoints as the sample points.
M_6 = ?
1 answer