So, I've been struggling to solve the following exercise:
$$ \int_0^1 \sqrt{4-x^2}\,dx $$
Most of the solutions I've seen online use substitution using $x = \cos(t)$ or $x = \sin(t)$, however I'm wondering how the substitution without $\cos$ or $\sin$ would work? Any help is appreciated!
Use the so-called Euler Substitution: $$\sqrt{-x^2+4}=xt+2$$ See here https://en.wikipedia.org/wiki/Euler_substitution