582

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 582

Source: 1998 Kochi Women's University entrance exam/Human Life and Enviromental Science

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

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