$4$

$10.(4$ pt$.)$ If $f(x)={\displaystyle \underset{0}{\overset{sinx}{}}}\sqrt[\phantom{2}]{1t^2}dt$ and $g(y)={\displaystyle \underset{3}{\overset{y}{}}}f(x)dx,$ find $g^{\text{'}\text{'}}(\frac{}{6}).$ Give an exact answer.

$11.(8$ pt$.)$ Suppose $f$ is an even function with ${\displaystyle \underset{0}{\overset{8}{}}}f(x)dx=9.$ Evaluate each integral. Failure to show every step of the algebraic process employed to find your solutions will result in a reduction of all possible points.

a$.{\displaystyle \underset{-1}{\overset{1}{}}}xf(x^2)dx$

b$.{\displaystyle \underset{-2}{\overset{2}{}}}{x}^{2}f(x^3)dx$

$12.(8$ pt$.)$ Evaluate the definite integral. Give an exact answer. Failure to show all algebraic steps to find the solution will result in a reduction of all possible points. This includes, but is not limited to$,$ showing u$-$substitution, change of variables, finding the correct antiderivative and evaluating.

${\displaystyle \underset{-\frac{1}{\sqrt[\phantom{2}]{3}}}{\overset{\frac{1}{\sqrt[\phantom{2}]{3}}}{}}}\frac{cos(ta{n}^{-1}(3x))}{19x^2}dx$