Subtopic: Numerical integration – trapezoidal and Simpson's rule
Question Statement:
Integration by trapezoidal method of log₁₀(x) with lower limit of 1 to upper limit of 3 using seven distinct values (equally covering the whole range) is _______
Official Answer Key:
0.5 to 0.6
Step-by-Step Solution & Explanation
With 7 equally spaced points over [1,3], the strip width h = (3−1)/6 = 0.3333. The x-values are 1, 1.333, 1.667, 2, 2.333, 2.667, 3, with y = log₁₀(x) at each. Trapezoidal rule: I = h·[ (y₀+y₆)/2 + Σ(y₁...y₅) ]. Evaluating: y = 0, 0.1249, 0.2219, 0.3010, 0.3680, 0.4260, 0.4771. I = 0.3333×[(0+0.4771)/2 + (0.1249+0.2219+0.3010+0.3680+0.4260)] = 0.3333×[0.2386+1.4418] = 0.560, within the accepted band 0.5–0.6.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.