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Today's calculation of Integral 269

Source: 2001 Osaka Medical College entrance exam

January 18, 2008

calculusintegrationgeometrytrigonometrycalculus computations

Problem Statement

For the curve

C: y = \frac {1}{1 + x^2}

, Let

A(\alpha ,\ f(\alpha)),\ B\left( - \frac {1}{\alpha},\ f\left( - \frac {1}{\alpha} \right)\right)\ (\alpha > 0).

Find the minimum area bounded by the line segments

OA,\ OB

and

C,

where

O

is the origin.
Note that you are not allowed to use the integral formula of

\frac {1}{1 + x^2}

for the problem.