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GATE 2016 CE (CE1) – Question 37

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 2 marks · Multiple choice

The value of $\int_0^\infty dx/(1+x^2)+\int_0^\infty (\sin x)/x\,dx$ is ______.

  1. $\pi/2$
  2. $\pi$
  3. $3\pi/2$
  4. 1

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Show answer and explanation

Correct answer: (B) $\pi$

Explanation

The integral of1/(1+x²) from0 to infinity is[arctan x]0∞=π/2. The Dirichlet integral of sin(x)/x over the same interval isπ/2. Adding yields **π, B**. Both are improper limits and the second converges conditionally rather than absolutely.