MathDB
Today's calculation of Integral 42

Source: 2000 Shiga University of Medical Science

June 12, 2005
calculusintegrationlimittrigonometrylogarithmscalculus computations

Problem Statement

Let 0<t<π20<t<\frac{\pi}{2}. Evaluate lim⁡t→π2∫0ttan⁡θcos⁡θln⁡(cos⁡θ)dθ\lim_{t\rightarrow \frac{\pi}{2}} \int_0^t \tan \theta \sqrt{\cos \theta}\ln (\cos \theta)d\theta
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