This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2004 Unirea, 4
Tags: limit , monotone , squeeze , limit of sequence of integrals , integration , calculus
Let be the sequence $ \left( I_n \right)_{n\ge 1} $ defined as $ I_n=\int_0^{\pi } \frac{dx}{x+\sin^n x +\cos^n x} . $ [b]a)[/b] Study the monotony of $ \left( I_n \right)_{n\ge 1} . $ [b]b)[/b] Calculate the limit of $ \left( I_n \right)_{n\ge 1} . $