Thank you for replying. I saw that myself a while ago and found what the maximum and minimum value of sin x over each of the 6 subintervals such that the upper sum sin x over partition P should be:
S(P) = ∑i=16 Δx ⋅max(sinx)i = (π/6) ⋅(1/2 + √3/2 + 1 + 1 + √3/2 + 1/2) = (π/6) ⋅ (3 + √3) ≈ 2,47...
Task in real analysis:
P is a uniform partition on [0, π] and is divided into 6 equal subintervals. Show that the lower and upper riemann sums of sin (x) over P is lesser than 1.5 and larger than 2.4 respectively.
My attempt at the solution:
The greates value and the least value of sin x over...