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Today's calculation of Integral 122

Source: Tokyo Metropolitan University entrance exam 1987

July 10, 2006
calculusintegrationtrigonometrylogarithmsgeometrycalculus computations

Problem Statement

Let x(t)=tan⁡t, y(t)=−ln⁡cos⁡t (−π2<t<π2).x(t)=\tan t ,\ y(t)=-\ln \cos t\ \left(-\frac{\pi}{2}<t<\frac{\pi}{2}\right). Find the area surrounded by the curve :x=x(t), y=y(t): x=x(t),\ y=y(t) and xx axis and the line x=1.x=1.
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