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Today's calculation of Integral 726

Source: 1976 Aoyama Gakuin University entrance exam

June 27, 2011
calculusintegrationgeometrylogarithmscalculus computations

Problem Statement

Let P(x, y) (x>0, y>0)P(x,\ y)\ (x>0,\ y>0) be a point on the curve C:x2−y2=1C: x^2-y^2=1. If x=eu+e−u2 (u≥0)x=\frac{e^u+e^{-u}}{2}\ (u\geq 0), then find the area bounded by the line OPOP, the xx axis and the curve CC in terms of uu.
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