GATE AG 2010 • Q30 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\int_{0}^{2} \int_{0}^{y} xy \, dx \, dy$ is:

Options:

  • (A) 0.5
  • (B) 1.0
  • (C) 2.0
  • (D) 4.0

Official Answer Key:

D

Step-by-Step Solution & Explanation

Inner integral (w.r.t. x, 0 to y): ∫₀ʸ xy dx = y·[x²/2]₀ʸ = y³/2. Outer integral: ∫₀² (y³/2) dy = [y⁴/8]₀² = 16/8 = 4.0. Section 2 — Farm Machinery

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