The range of sin(x) is the interval [-1, 1], which is also the domain of arccos(x). I'm not being able to figure out how that will affect ##\mathrm{d}u##. What will ##\mathrm{d}u## be if ##u = \arccos(\sin x)##?
Ok, I tried it with integration by parts with ##u = \cos^{−1}(\sin(x))## and ##\mathrm{d}v = \mathrm{d}x##, which gives us ##\mathrm{d}u = \frac{−\cos(x)}{\sqrt{1−\sin^2 x}}\mathrm{d}x = −\mathrm{d}x## and ##v=x##.
The integral becomes ##x\cos^{−1}(\sin(x)) + \int x \mathrm{d}x =...
Here's the problem: ##\int_0^{2\pi} \cos^{-1}(\sin(x)) \mathrm{d}x##
If I do the substitution ##u = \sin(x)##, both the limits of integration become 0 and the integral would result in 0. But the graph of the function tells me the area isn't 0. Where am I going wrong?
TL;DR Summary: Is "Quantum Mechanics Demystified" a good book for a beginner for self-studying?
I'm a layman with background in high school physics and undergrad calculus. Is "Quantum Mechanics Demystified" by David McMahon a good book for self-studying and learning quantum mechanics?
Just saw a claim online that "Dawkins isn't a recognized scientist", which seemed like a strange claim. It made me wonder: how much research did Dawkins do over the years? Can you provide some references to his list of researches?
Yes, that's one of the types I am talking about. A slightly different case that I am also interested in is where someone's heart stopped and then started again spontaneously without medical intervention.
This is the one I am interested in. Before the revival, the individual is dead. They just...
Google didn't help much. The results were about near-death experiences, and from sources like buzzfeed, boredpanda etc. Any ideas on how to narrow down the search?
Edit: Just found out about Lazarus Syndrome.
I am looking for cases (if any) where patients were pronounced dead by doctors and then came back to life. Are there any such cases? I am not looking for cases of near-death experiences. I'm also not looking for cases where patients were mistakenly declared dead when they were still alive.