the last question on a Harvard-MIT Math Tournament!

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This is the last question of the calculus part of the 2002 Harvard MIT Math Tournament #HMMT. I first thought this is a hard integral question since I was amazed by the HMMT official solution. However, I did come up with an easier solution. Here's the question: we are given f(2x)=3f(x) and the integral of f(x) from 0 to 1 is 1. We have to find the value of the integral of f(x) from 1 to 2. This question is a good challenge for calculus 1 and AP calculus students on integral properties and u-substitution. Try all the problems here: https://hmmt-archive.s3.amazonaws.com...

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0:00 the question!
0:32 Harvard-MIT Math Tournament official solution
7:23 learn more integrals on Brilliant!
8:22 my solution
10:36 final thoughts & you try this question