542

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 542

Source: 1980 Kobe University entrance exam/Science

Find continuous functions

f(x),\ g(x)

which takes positive value for any real number

x

, satisfying g(x)\equal{}\int_0^x f(t)\ dt and \{f(x)\}^2\minus{}\{g(x)\}^2\equal{}1.

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