Subdivide the interval 0 t 22 into n subintervals of length t = 22/n seconds.

Subdivide the interval 0 ≤ t ≤ 22 into n subintervals of length Δt = 22/n seconds. Let ti be a point in the ith subinterval.

(a) Show that (R/60)Δt ≈ [number of liters of blood flowing past the monitoring point during the ith time interval].

b) Show that c(ti)(R/60)Δt ≈ [quantity of dye flowing past the monitoring point during the ith time interval].

(c) Assume that basically all the dye will have flowed past the monitoring point during the 22 seconds. Explain why D ≈ (R/60)[c(t₁) + c(t₂) +. . .+ c(t_n)]Δt, where the approximation improves as n gets large.

(d) Conclude that D = ∫₀²² (R/60)c(t) dt, and solve for R.