did you know there& #39;s a formula for computing integrals of inverse functions? Think back: did this useful result appear in your basic calculus courses? 1/n
Probably not. How did this result somehow get weeded out of the curriculum while all these other Newton/Euler era integration techniques got passed down?
Guess what: IT& #39;S A RELATIVELY RECENT RESULT. In full generality it first appeared publicly in 1965. 2/n
Guess what: IT& #39;S A RELATIVELY RECENT RESULT. In full generality it first appeared publicly in 1965. 2/n
Even the special case dates from 1904?! Unbelievable. Nobody wrote down and published a proof until 1994!
There really is so much low hanging fruit in mathematics. You just need to be willing to ask silly questions. 3/3
There really is so much low hanging fruit in mathematics. You just need to be willing to ask silly questions. 3/3
Actually, one more thing. Looking at this formula, there must be some connection to integration by parts. We have a thing we want to integrate on the LHS, and on the RHS a product of an antiderivative (of dy) with the function, minus something computed by an integral. 1/n& #39;
Now consider this tidbit from the wikipedia article (everything in this thread is from wikipedia):
2/n& #39;
2/n& #39;
In research, one must scrutinize the literature mercilessly. We therefore type "integration by parts" into the wikipedia search bar and scroll until we see something familiar. And lo and behold:
3/n& #39;
3/n& #39;