I found this problem in a short article in the College Mathematics Journal a while back and have been showing my calculus students since. It's a short proof using the Fundamental Theorem of Calculus, but not the part most people use. I recorded a video going through the proof and thought I'd share it.
https://www.youtube.com/watch?v=ptMpRwqc9zY
Sorry for the click-baity title, but I like the fact that this uses the part of the Fundamental Theorem of Calculus that is sometimes forgotten by students. I thought this little example was a cute way of using this part of the theorem to get to a result that Calculus 1 students might not see otherwise.
Obviously the trigonometric substitution method is a fine option as well, but I like this problem for not needing to rely on any tricky antidifferentiation techniques.
Here's the link to the short article where I found this: https://doi.org/10.4169/college.math.j.46.4.299
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