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Today's calculation of Integral 609

Source:

June 2, 2010
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Prove that for positive number tt, the function F(t)=∫0tsin⁡x1+x2dxF(t)=\int_0^t \frac{\sin x}{1+x^2}dx always takes positive number.
1972 Tokyo University of Education entrance exam
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