A Genius Integral Solved with Feynman’s Trick скачать в хорошем качестве

A Genius Integral Solved with Feynman’s Trick

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. Please subscribe to Calculus Diaries for more elegant calculus and problem-solving techniques. Don't forget to turn on the notification bell so you won't miss any uploads from Calculus Diaries. #calculus #integrationtechniques #integralcalculus