MathDB
Today's calculation of Integral 666

Source:

January 12, 2011
calculusintegrationfunctiontrigonometrylogarithmscalculus computations

Problem Statement

Let f(x)f(x) be a function defined in 0<x<π20<x<\frac{\pi}{2} satisfying:
(i) f(π6)=0f\left(\frac{\pi}{6}\right)=0
(ii) f′(x)tan⁡x=∫π6x2cos⁡tsin⁡tdtf'(x)\tan x=\int_{\frac{\pi}{6}}^x \frac{2\cos t}{\sin t}dt.
Find f(x)f(x).
1987 Sapporo Medical University entrance exam
Back to ProblemsView on AoPS