Theory question 103
IntegrationUsing the trapezium rule with seven ordinates, evaluate, correct to three decimal places, ∫2436 1/√(x2 − 2) dx
Show the model answer
Model answer
Seven ordinates means 6 strips: h = (36 − 24)/6 = 2.
x: 24, 26, 28, 30, 32, 34, 36; y = 1/√(x² − 2): 0.04174, 0.03852, 0.03576, 0.03337, 0.03128, 0.02944, 0.02780.
Area ≈ (h/2)[y₀ + y₆ + 2(y₁ + … + y₅)] = 1 × [0.06954 + 2(0.16837)] ≈ 0.406.
(If the limits are 2.4 to 3.6, as the book's working uses: h = 0.2, y = 0.51571, 0.45835, 0.41380, 0.37796, 0.34837, 0.32342, 0.30206, and the integral ≈ 0.466.)
Explanation
Seven ordinates give six equal strips.