Project ForgeEngineering Mathematics
Calculus
GATE 2016
Hard
The error in numerically computing the integral ∫₀^π (sin x + cos x) dx using the trapezoidal rule with three intervals of equal length between 0 and π is __________.
0.185(± 0.01 accepted)
Explanation
True value: [-cos x+sin x]₀^π = (1+0)-(-1+0)=2. Trapezoidal with h=π/3: f(0)=1, f(π/3)=1.366, f(2π/3)=0.366, f(π)=-1. Sum=(h/2)[f0+2f1+2f2+f3]=(0.5236)(1+2.732+0.732-1)=0.5236×3.464≈1.814. Error = 2-1.814 ≈ 0.186.
Source: GATE ME 2016 Set-2 (2016)
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