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Today's calculation of integral 101

Source: Osaka Institute of technology entrance exam 1985

June 5, 2006
calculusintegrationcalculus computations

Problem Statement

Thank you very much, vidyamanohar. I will continue to post problems. For n>2,n>2, prove the following inequality. 12<∫01211−xndx<π6. \frac{1}{2}<\int_0^{\frac{1}{2}} \frac{1}{\sqrt{1-x^n}} dx<\frac{\pi}{6}.
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