I need to integrate sqrt(1-(x^2))
I know that the reciprical of this integrates to arcsin(x) + k but I don't know how I can relate this.
Any help would be much appreciated
Hello, kinhew93!
$\displaystyle I \;=\; \int \sqrt{1-x^2}\,dx$
It should be obvious that this requires Trig Substitution.
Let $\displaystyle x \,=\,\sin\theta \quad\Rightarrow\quad dx \,=\,\cos\theta\,d\theta$
. . And: .$\displaystyle \sqrt{1-x^2} \:=\:\sqrt{1-\sin^2\!x} \:=\:\sqrt{\cos^2\!x} \:=\:\cos x$
Substitute: .$\displaystyle I \;=\;\int\cos\theta(\cos\theta\,d\theta) \;=\;\int\cos^2\!\theta\,d\theta \;=\;\tfrac{1}{2}\int (\cos2\theta - 1)\,d\theta$
Can you continue?