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Today's calculation of integral 110

Source: Kochi University entrance exam/Science 2003

June 7, 2006
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

Prove the following inequality. 1≤∫0π21−sin⁡3x dx≤12{2+ln⁡(1+2 )} 1\leq \int_0^{\frac{\pi}{2}} \sqrt{1-\sin ^ 3 x} \ dx\leq \frac{1}{2}\{\sqrt{2}+\ln (1+\sqrt{2}\ ) \}
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