GATE AG 2014 • Q40 MCQ • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\int_{0}^{\pi/2} \frac{\cos^2 x}{1+\sin x} \, dx$ is:

Options:

  • (A) 0
  • (B) π/2 − 1
  • (C) 2
  • (D) π/2 + 1

Official Answer Key:

B

Step-by-Step Solution & Explanation

cos²x = 1 − sin²x = (1−sinx)(1+sinx), so cos²x/(1+sinx) = (1 − sinx). ∫₀^(π/2) (1 − sinx) dx = [x + cosx]₀^(π/2) = (π/2 + 0) − (0 + 1) = π/2 − 1. Answer: (B). Section 2 Machine Design

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