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Today's calculation of Integral 752

Source: 2011 Nagoya City University entrance exam/Medicine

September 13, 2011
calculusintegrationinductioncalculus computations

Problem Statement

Find fn(x)f_n(x) such that f1(x)=x, fn(x)=∫0xtfn−1(x−t)dt (n=2, 3, ⋯ ).f_1(x)=x,\ f_n(x)=\int_0^x tf_{n-1}(x-t)dt\ (n=2,\ 3,\ \cdots).
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