【京都帝國大學】積分の難問に挑戦！【戦前入試問題】

⭐️ "Oshie Math" allows you to ask Hayashi unlimited questions for a fixed monthly fee. You can try asking questions for free once! https://oshiemath.com/ ⭐️ "Hayashi Math Class," a specialized mathematics school where you can receive direct instruction from Hayashi. Please come for a trial lesson and consultation! https://hayashi-math.com/ [Now on sale at Amazon, bookstores, etc.!] Tokyo Imperial University entrance exam questions are now available in book form! "100 Deep and Difficult Questions from the University of Tokyo Entrance Exam Mathematics 100 Years Ago" https://amzn.to/3d39zgN Although it is only for the University of Tokyo entrance exam, we have collected some interesting questions and provided detailed explanations. Please take a look! ✅ Official LINE for students taking entrance exams to top universities: https://lin.ee/lI7n1SJ Subscriber benefits & live streams for test-takers available ℹ️ Shunsuke Hayashi's Profile https://hayashishunsuke.com/profile/ ・Eihigashi Junior High School → Chikuma High School → University of Tokyo, Faculty of Science, Graduated from the Department of Physics ・Scored 90% on the second-stage mathematics exam at the University of Tokyo and passed the exam ・2014 Japan Physics Olympiad Gold Medal ・Placed first in the 2014 University of Tokyo Practical Mock Exam Physics ℹ️ Please Note ・The explanations are Shunsuke Hayashi's own and are not official university information. ・Amazon Associates links are used for book recommendations. This time, we're looking at a problem from the Kyoto Imperial University Department of Physics in 1923. It's a simple indefinite integral, but it's quite difficult. Not only is it difficult, but the integration method and results change depending on the relative magnitudes of the two constants a and b. This is a difficult problem that would not be out of place in the entrance exams of today's most prestigious universities. If you are a candidate aiming for the top level of science, be sure to give it a try! ▶︎Correction: The integral result after partial fraction decomposition requires an absolute value symbol! We apologize for the error and have made this correction. The contents of the log of the final result (fractions) also require an absolute value symbol. ---------- Table of Contents 00:00 Kyoto University Entrance Exam in 1923 (Taisho 12) 01:00 Case of a = b (Easy) 02:51 Case of a ≠ b → Rewriting the integral 06:48 Case distinction based on the magnitude relationship between a and b 09:02 0 a b → Partial fraction decomposition 11:15 Integrate each decomposed term 12:28 Organizing the results (log of division) 14:08 Summary of the case of 0 a b 15:37 0 b a → Use arctan 18:23 Transform variables and perform integration 20:25 Summary of the case of 0 b a 22:39 Conclusion