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Today's calculation of Integral 863

Source: 1981 Tokyo Institute of Technology entrance exam

January 27, 2013
calculusintegrationtrigonometrylimitderivativeinequalitiescalculus computations

Problem Statement

For 0<t≤10<t\leq 1, let F(t)=1t∫0π2t∣cos⁡2x∣ dx.F(t)=\frac{1}{t}\int_0^{\frac{\pi}{2}t} |\cos 2x|\ dx.
(1) Find lim⁡t→0F(t).\lim_{t\rightarrow 0} F(t).
(2) Find the range of tt such that F(t)≥1.F(t)\geq 1.
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