Mathematics - Indefinite Integration Question with Solution | TestHub

In general the integral is $(ab{)}^{-1}{\tan }^{-1}((a/b)\tan x)+C$. Thus $ab=12$ and $a/b=3$, giving $(a,b)=(6,2)$ or $(-6,-2)$. As $x$ varies, $a\sin x+b\cos x$ ranges through $[-\sqrt{40},\sqrt{40}]$, so all four values are possible.