Project ForgeEngineering Mathematics
Calculus
GATE 2021
Medium
Value of ∫₄^5.2 ln x dx using Simpson's one-third rule with interval size 0.3 is (round off to two decimal places).
1.83(± 0.05 accepted)
Explanation
With h=0.3, nodes are 4, 4.3, 4.6, 4.9, 5.2 (n=4 intervals). Simpson's 1/3 rule: I=(h/3)[f0+f4+4(f1+f3)+2f2] = (0.3/3)[ln4+ln5.2+4(ln4.3+ln4.9)+2ln4.6] ≈ 0.1×[3.0350+4×3.0479+3.0521] ≈ 1.83.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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