IMathAS-libretexts

Let

\displaystyle {F}{\left({x}\right)}={\int_{{0}}^{{{x}}}}{\sin{{\left({6}{t}^{{2}}\right)}}}\ {\left.{d}{t}\right.}

.
Find the MacLaurin polynomial of degree 7 for

\displaystyle {F}{\left({x}\right)}

.

Use this polynomial to estimate the value of

\displaystyle {\int_{{0}}^{{{0.68}}}}{\sin{{\left({6}{x}^{{2}}\right)}}}\ {\left.{d}{x}\right.}