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Today's calculation of Integral 203

Source: Tokyo Instutute of Technology entrance exam 1967

May 15, 2007
calculusintegrationtrigonometrycalculus computations

Problem Statement

Let α, β\alpha ,\ \beta be the distinct positive roots of the equation of 2x=tan⁡x2x=\tan x. Evaluate the following definite integral. ∫01sin⁡αxsin⁡βx dx\int_{0}^{1}\sin \alpha x\sin \beta x\ dx
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