Project ForgeEngineering Mathematics
Calculus
GATE 2020
Medium
For the integral ∫(0 to π/2) (8+4cos x) dx, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is __________ (round off to one decimal place).
5.2 %(± 0.3 accepted)
Explanation
True value: ∫(8+4cos x)dx from 0 to π/2 = [8x+4sin x] = 4π+4 ≈ 16.566. Trapezoidal (endpoints only): f(0)=12, f(π/2)=8; T=(π/2)/2×(12+8)=5π≈15.708. Absolute % error = |16.566−15.708|/16.566×100 ≈ 5.18%, rounding to 5.2%.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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