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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

If ∫_0^1 ( ∑_ r=1 ^ 2013 (x)/(x^2+r^2) ) ( _ r=1 ^ 2013 ( x^2+r²) )...

If \int_0^1 \left( \sum_{r=1}^{2013}\frac{x}{x^2+r^2} \right) \left( \prod_{r=1}^{2013} (x^2+r²) \right) dx =\frac{1}{2} \left[ \prod_{r=1}^{2013} (1+r²) - k² \right] then k=k =

Options

  1. A2013
  2. B2013!
  3. C201322013^2
  4. D201320132013^{2013}

Correct answer

B. 2013!

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