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Today's calculation of Integral 161

Source: Kogakuin University entrance exam 1992

October 18, 2006
calculusintegrationfunctiontrigonometrylogarithmscalculus computations

Problem Statement

Find the differentiable function f(x)f(x) such that f(x)=−∫0xf(t)tan⁡t dt+∫0xtan⁡(t−x) dt (∣x∣<π2).f(x)=-\int_{0}^{x}f(t)\tan t\ dt+\int_{0}^{x}\tan (t-x)\ dt\ \left(|x|<\frac{\pi}{2}\right).
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