Function f is known at the following points: The value of 03 f(x)\,dx computed using the trapezoidal rule is A) 8.983 B) 9.003 C) 9.017 D) 9.045

Official answer: D) 9.045. Explanation: From the given table, step size h = 0.3, x0 = 0, xn = 3.0 with n = 10 subintervals. The Trapezoidal Rule formula is: x0xn f(x)\,dx h2 [ f(x0) + f(xn) + 2 i=1n-1 f(xi) ] Here: - f(x0) = f(0) = 0 - f(xn) = f(3.0) = 9.00 - Sum of intermediate terms: i=19 f(xi) = 0.09 + 0.36 + 0.81 + 1.44 + 2.25 + 3.24 + 4.41 + 5.76 + 7.29 = 25.65 Applying the formula: 03 f(x)\,dx 0.32 [ 0 + 9.00 + 2(25.65) ] 03 f(x)\,dx 0.15 [9.00 + 51.30] = 0.15 60.30 = 9.045 Hence, the correct option is (D).

Engineering Mathematics · Calculus

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GATE CSE 2013 Q23 · MCQ · 1 mark

Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is

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Calculus in GATE CS tests single-variable differential and integral calculus, foundational limit evaluations, continuity and differentiability of piecewise/absolute-value functions, and mean value theorems (Rolle's and LMVT). Earlier years (2012-2015) also included numerical methods such as Newton-Raphson, Bisection, and Trapezoidal/Simpson's rules, whereas recent papers (2020-2026) focus heavily on analytical properties: odd/even symmetry in single and multiple integrals, boundary extrema, points of non-differentiability, and MSQ-based structural analyses of functions.

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Engineering Mathematics · Calculus

Official IIT answer key · IIT Bombay · Audited Aug 2026

Take topic test

GATE CSE 2013 Q23 · MCQ · 1 mark

Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is

Select an option to check

Key concept

Calculus

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Calculus

Full Calculus guide →

More on Calculus

All 40 questions on Calculus →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is

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Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is

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Function fff is known at the following points: The value of ∫03f(x) dx\int_0^3 f(x)\,dx∫03​f(x)dx computed using the trapezoidal rule is

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Function fff is known at the following points: The value of ∫03f(x) dx\int_0^3 f(x)\,dx∫03​f(x)dx computed using the trapezoidal rule is

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Check you can still solve Calculus under a clock

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Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is

Function $f$ is known at the following points: The value of $\int_0^3 f(x)\,dx$ computed using the trapezoidal rule is