A Genius Integral Solved with Feynman’s Trick
Автор: Calculus Diaries
Загружено: 2026-01-14
Просмотров: 202
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This integral looks intimidating at first glance, but with Feynman’s trick (differentiation under the integral sign), it collapses into something surprisingly elegant.
In this video, we evaluate the integral from 0 to pi/2 of arctan(a*tan(x))/tan(x) dx and show that it simplifies beautifully to pi/2*ln(1+a) for values of a greater than -1.
This is a classic example of why Richard Feynman’s technique is so powerful when dealing with parameter-dependent integrals.
Topics covered in this video:
1. Feynman’s trick (differentiation under the integral sign)
2. Trigonometric integrals
3. Partial fraction decomposition
4. Parameter integrals
5. Elegant calculus techniques
If you enjoy beautiful integrals, parameter-dependent integrals, clever substitutions, and competition-style tricks, this one’s for you.
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#calculus #integrationtechniques #integralcalculus
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