MathDB
Today's calculation of Integral 45

Source: 1999 Tokyo University of Science

June 15, 2005
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Find the function f(x)f(x) which satisfies the following integral equation. f(x)=∫0xt(sin⁡t−cos⁡t)dt+∫0π2etf(t)dtf(x)=\int_0^x t(\sin t-\cos t)dt+\int_0^{\frac{\pi}{2}} e^t f(t)dt
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