${\displaystyle \underset{3}{\overset{6}{}}}sin(\sqrt[\phantom{2}]{x})dx,n=6$

Q$6$

etermine whether the Integral is convergent or divergent. If it is convergent, laluate it$.($If the quantity diverges, enter DIVERGES$)$

${\displaystyle \underset{-}{\overset{0}{}}}\frac{x}{(x^2+4{)}^3}dx$

Q$7$

Find the exact length of the polar curve.

$r=5cos(),0$

Q$8$

Consider the following parametric curve.

$x=sin(t),y=co{s}^2(t)$;$,(\frac{\sqrt[\phantom{2}]{3}}{2},\frac{1}{4})$

Find an equation of the tangent to the curve at the given point