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Today's calculation of Integral 690

Source: 2011 Tokyo Metropolitan University entrance exam, Problem 2,

March 13, 2011
calculusintegrationtrigonometryvectorcalculus computations

Problem Statement

Find the maximum value of f(x)=∫01tsin⁡(x+πt) dtf(x)=\int_0^1 t\sin (x+\pi t)\ dt.
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