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Today's calculation of Integral 283

Source: 1977 Tokyo Institute of Technology entrance exam

January 24, 2008

calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

f(x)

is a continuous function with the piriodicity of

2\pi

and

c

is a positive constant number. Find

f(x)

and

c

such that \int_0^{2\pi} f(t \minus{} x)\sin tdt \equal{} cf(x) with f(0) \equal{} 1 for all real numbers

x