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Today's calculation of Integral 225

Source: Kogakuin University entrance exam 2007

September 16, 2007
calculusintegrationgeometrylogarithmsratioinequalitiesfunction

Problem Statement

2 Points P(a, 1a), Q(2a, 12a) (a>0) P\left(a,\ \frac{1}{a}\right),\ Q\left(2a,\ \frac{1}{2a}\right)\ (a > 0) are on the curve C: y \equal{}\frac{1}{x}. Let l, m l,\ m be the tangent lines at P, Q P,\ Q respectively. Find the area of the figure surrounded by l, m l,\ m and C C.
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