Approximate the value of ∫ab f (x)dx, where f (x) ≥ 0, by dividing the interval a ≤ x ≤ b into four subintervals and constructing five rectangles. (See Fig. 14.) Note that the width of the three inside rectangles is Δx, while the width of the two outside rectangles is Δx/2. Compute the sum of the areas of these five rectangles and compare this sum with the trapezoidal rule for n = 4.

Transcribed Image Text:

(ad,./(a0)) Δι 2 (αγ.f(ay)) Δια + αι Δ 2 Δ.χ. Δα a = do ag ag Figure 14 Another view of the trapezoidal rule. y = f(x) aj = b