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Today's calculation of Integral 263

Source: 1981 Tokyo Institute of Technology entrance exam

January 10, 2008
calculusintegrationtrigonometrylimitcalculus computations

Problem Statement

Let F(t)\equal{}\frac{1}{t}\int_0^{\frac{\pi}{2}t}|\cos 2x|\ dx for 0<t≤1. 0<t\leq 1. (1) Find lim⁡t→0F(t). \lim_{t\rightarrow 0} F(t). (2) Find the range of t t such that F(t)≥1. F(t)\geq 1.
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