Asked by Tara
(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 = ?
R_6 = ?
(b) Repeat part (a) with midpoints as the sample points.
M_6 = ?
Answers
Answered by
oobleck
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.