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GATE 2021 CE (CE2) – Question 56

Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 2 marks · Numerical answer

Integrate $f(x)=10x-20x^2$ from 0 to 0.5 by the trapezoidal rule with five equal subdivisions. Round to two decimals.

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Correct answer: .38 to .42

Explanation

Step h=0.1 gives ordinates 0,0.8,1.2,1.2,0.8,0. The composite trapezoidal sum is $0.1[(0+0)/2+0.8+1.2+1.2+0.8]=\mathbf{0.40}$. The exact integral 0.41667 is not the requested numerical approximation.