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Limit of an integral

Source: IMC 2003 day 2 problem 2

October 14, 2005
calculusintegrationlimittrigonometrylogarithmsinequalitiesreal analysis

Problem Statement

Evaluate lim⁡x→0+∫x2xsin⁡m(t)tndt\lim_{x\rightarrow 0^+}\int^{2x}_x\frac{\sin^m(t)}{t^n}dt. (m,n∈Nm,n\in\mathbb{N})
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