Question

Find F (x) from the given F'(x)
F'(x) = $1/si{n}^2$ x, whose graph passes through the point A $(\pi /6,0)$

Answer 1

$F^{\prime }\left(x\right)={\csc }^{2}x$

$\int F^{\prime }\left(x\right)dx=-\cot x+c=F\left(x\right)$

Given that $F\left(\frac{\pi }{6}\right)=0$

$F\left(\frac{\pi }{6}\right)=-\sqrt{3}+c=0\Rightarrow c=\sqrt{3}$

$F\left(x\right)=\sqrt{3}-\cot x$