Let $\displaystyle F(x) = \int_0^{x} \sin(6 t^2) \ dt$.
Find the MacLaurin polynomial of degree 7 for $F(x)$.

Use this polynomial to estimate the value of $\displaystyle \int_0^{0.64} \sin(6 x^2) \ dx$.


Note: your answer to the last part needs to be correct to 9 decimal places.