Mark M. answered • 01/20/19

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

Δx = (9-1)/n = 8/n

Divide the interval [1,9] into n equal subintervals each of width Δx.

Right endpoint of first interval = 1 + Δx

Right endpoint of 2nd interval = 1 + 2Δx

Right endpoint of 3rd interval = 1 + 3Δx......

Right endpoint of last interval = 1 + nΔx = 9

R_{n} = Σ_{(i = 1 to n)} [f(1 + iΔx)Δx]

∫_{(from 1 to 9)}f(x)dx = lim_{n→∞}R_{n} =

lim_{n→∞}[∑_{(i = 1 to n)}{(1 + 8i/n)^{-3}(8/n)}]