Assume that $sin(x)$ equals its Maclaurin series for all $x.$

Use the Maclaurin series for $sin(3x^2)$ to evaluate the integral

${\displaystyle \underset{0}{\overset{0\mathrm{.}78}{}}}sin(3x^2)dx$

Your answer will be an infinite series. Use the first two terms to estimate its value.