Today's calculation of Integral 529
Source: 2006 Ochanomizu Women University entrance exam/Mathematics
January 14, 2010
calculusintegrationinequalitiestrigonometrycalculus computations
Problem Statement
Prove that the following inequality holds for each natural number .
\int_0^{\frac {\pi}{2}} \sum_{k \equal{} 1}^n \left(\frac {\sin kx}{k}\right)^2dx < \frac {61}{144}\pi