using integration by parts to hate myselfpic.twitter.com/mLwr37sHfU
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What a charming calculation!
thanks! here's the anti-climactic story behind ithttps://twitter.com/InertialObservr/status/1215091007093526533?s=20 …
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at first i thought it was silly.. it never crossed my mind that it could be a cute pedagogical example for undergrads/high schoolers
Thanks. Twitter will use this to make your timeline better. UndoUndo
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It’s a nice example of a common trick: sometimes one can evaluate a quantity Q by manipulating it to yield an expression with that same Q on the right hand side. Then solve for Q. Boom. You did this in your solution for that ln(sin x) definite integral I tweeted a while back.
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Another example: summing an infinite geometric series. Let Q = 1+r+r^2+r^3+... . Observe that Q = 1+r(1+r+r^2+..) = 1 + rQ. So by manipulating Q, we got Q to appear on the right side. Solve for Q. Get Q = 1/(1-r), which is correct! (assuming the series converges, of course)
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