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Today's calculation of Integral 828

Source: 2012 Miyagi University of Education entrance exam

July 1, 2012
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Find a function f(x)f(x), which is differentiable and f′(x)f'(x) is continuous, such that ∫0xf(t)cos⁡(x−t) dt=xe2x.\int_0^x f(t)\cos (x-t)\ dt=xe^{2x}.
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