[Daily puzzle] Integral \ stacker news ~science

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[Daily puzzle] Integral

684 sats \ 11 comments \ @south_korea_ln 31 Oct science

Need to work on some other stuff soon, so falling back on this one I had prepared a while ago for such an occasion.

Can you solve this integral?

Previous iteration: #746521 (answer in #746671).

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101 sats \ 2 replies \ @south_korea_ln OP 2 Nov

First, break the integral into two parts as

Using the

substitution, the first integral becomes

while the second becomes

With the additional substitution

, the final integral above becomes

so that the original integral is equal to

0 sats \ 1 reply \ @SimpleStacker 2 Nov

Curious as to how the hint was related

21 sats \ 0 replies \ @south_korea_ln OP 2 Nov

Ah i was trying to hint at the fact one had to do another substitution. You had already done one, i was trying to tell you to do another one. Instead of switching to integration by parts. Maybe not the best hint ;)

300 sats \ 2 replies \ @SimpleStacker 31 Oct

This is as far as I got. Maybe someone else can take it the rest of the way

The left term can be easily calculated.

For the right term, let

Using integration by parts, you can show that:

Starting at

which is easy to calculate, you can use the above algorithm to eventually calculate

to find the answer.

0 sats \ 1 reply \ @south_korea_ln OP 1 Nov

For the right term, one can do another substitution. Will write it out later.

0 sats \ 0 replies \ @south_korea_ln OP 2 Nov

See here: #750702

0 sats \ 0 replies \ @south_korea_ln OP 31 Oct

Hint: never change a winning team...

0 sats \ 0 replies \ @0xbitcoiner 31 Oct

I bet it's greater than zero and less than one! Ahhhah

0 sats \ 2 replies \ @Aardvark 31 Oct

I'm sticking with 42. It's going to be correct eventually.

10 sats \ 1 reply \ @south_korea_ln OP 31 Oct

Just for you, I'll make sure that it'll happen, one day... just need to stick around, long enough

0 sats \ 0 replies \ @Aardvark 31 Oct

I'll do my best!