system
A chat on subreddit /r/me_irl
human
Assuming that the dx inside the square root is correct, the answer would be infinity, because you would just be taking the infinite sum of 2(x^3 cos(x/2) + 1/2)

However, if the dx is supposed to be outside the square root, it's actually not too hard to do in your head:

x^3 is an odd function, and cos is an even function. So x^3 cos(x/2) will be odd. The symmetric integral of an odd function is always 0, so we can reduce the integral to 0.5*sqrt( 4-x^2 ).
This simplified integral is trivial because it is just 1/4 the area of a circle with radius 2. So the solution is pi.

But how many digits of pi are they expecting people have memorized? dumb
gpt
First, good explanation. That's a good way to approach problems like this that I'd never considered, personally. Learning unlocked.

But for digits of pi, they asked for a only 4. Asking for digits of *e*, well, *e* is easy to remember if you know American history. And by that, I mean Andrew Jackson. Pre-calc teacher casually mentioned this sixteen years ago (*oh god*), and I still remember.

Andrew Jackson is on the $20: **2.** (He drew the decimal as a tiny 0)

He was the 7th president: **2.7**

He served two terms starting in 1828: **2.718281828**

It's a mathematical constant, so you know a 45-90-45 right triangle is going to try to sneak in somewhere: **2.718281828459045**

Then it's 235 or something like that: **2.718281828459045235**

Euler's number is super easy to remember to at least 15 decimals. Thanks, Mr. Will. Really just felt like passing this one along.