olymmath

Putnam 1953 A4

  • Session A
  1. From the identity ∫0π/2log⁡sin⁡2xdx=∫0π/2log⁡sin⁡xdx+∫0π/2log⁡cos⁡xdx+∫0π/2log⁡2dx\begin{aligned} \int_{0}^{\pi / 2} \log \sin 2 x d x & =\int_{0}^{\pi / 2} \log \sin x d x \\ & +\int_{0}^{\pi / 2} \log \cos x d x+\int_{0}^{\pi / 2} \log 2 d x \end{aligned} deduce the value of ∫0π/2log⁡sin⁡xdx\int_{0}^{\pi / 2} \log \sin x d x

Dataset text PutnamGAP. Quoted with source.

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