MathDB

529

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 529

Source: 2006 Ochanomizu Women University entrance exam/Mathematics

1/14/2010
Prove that the following inequality holds for each natural number n n. \int_0^{\frac {\pi}{2}} \sum_{k \equal{} 1}^n \left(\frac {\sin kx}{k}\right)^2dx < \frac {61}{144}\pi
calculusintegrationinequalitiestrigonometrycalculus computations