Engineering Mathematics · Calculus
Official IIT answer key · IIT Kharagpur · Audited Aug 2026
GATE CSE 2014 Set 3 Q46 · MCQ · 2 marks
Key concept
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Topic notes
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.
Full Calculus guide →With respect to the numerical evaluation of the definite integral, K = ab x2 \, dx, where a and b are given, which of the following statements is/are TRUE? I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral. II) The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
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