Today's calculation of Integral 582
Source: 1998 Kochi Women's University entrance exam/Human Life and Enviromental Science
March 13, 2010
calculusintegrationtrigonometryinequalitiescalculus computations
Problem Statement
Prove the following inequality.
\frac{\pi}{4}\sqrt{\frac{3}{2}\plus{}\sqrt{2}}<\int_0^{\frac{\pi}{2}} \sqrt{1\minus{}\frac 12\sin ^ 2 x}\ dx<\frac{\sqrt{3}}{4}\pi