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Today's calculation of Integral 624

Source:

July 8, 2010
calculusintegrationfunctiontrigonometryreal analysiscalculus computations

Problem Statement

Find the continuous function f(x)f(x) such that the following equation holds for any real number xx.
∫0xsin⁡t⋅f(x−t)dt=f(x)−sin⁡x.\int_0^x \sin t \cdot f(x-t)dt=f(x)-\sin x.
1977 Keio University entrance exam/Medicine
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