$6$

$4,7$

$5.(20$ pts$.)$ A Gaussian formula with degree of precision $5$ is given by

${\displaystyle \underset{-1}{\overset{1}{}}}f(x)dx$~~$\frac{1}{9}[5f(-\sqrt[\phantom{2}]{\frac{3}{5}})+8f(0)+5f(\sqrt[\phantom{2}]{\frac{3}{5}})]$

Use this formula to approximate the following integral. Write down the expression for the numerical ture but do not evaluate.

${\displaystyle \underset{0}{\overset{4}{}}}sin(x^2)dx$