GATE CE 2023 Set 1 — Question 36

MCQ+2 / -0.67MediumTrapezoidal RuleNumerical Integration & ODEsEngineering Mathematics

Engineering Mathematics → Numerical Integration & ODEs → Trapezoidal Rule

Last updated 5 September 2026

Question

f(x)

Correct answer (A) the numerical value of the area obtained using the trapezoidal rule will be less than the actual Solution The figure shows a function that is concave down (hill-shaped). In numerical integration using the trapezoidal rule, the curve is approximated by straight-line segments (chords) connecting the observed points. For a concave-down function, these chords always lie below the actual curve. Consequently, the area of the trapezoids formed under these chords will be less than the actual area under the smooth curve. Therefore, the numerical value obtained using the trapezoidal rule will be less than the actual area. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) the numerical value of the area obtained using the trapezoidal rule will be less than the actual Solution The figure shows a function that is concave down (hill-shaped). In numerical integration using the trapezoidal rule, the curve is approximated by straight-line segments (chords) connecting the observed points. For a concave-down function, these chords always lie below the actual curve. Consequently, the area of the trapezoids formed under these chords will be less than the actual area under the smooth curve. Therefore, the numerical value obtained using the trapezoidal rule will be less than the actual area.

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