(Solved): Assume that \( \sin (x) \) equals its Maclaurin series for all \( x \). Use the Maclaurin series fo ...

Assume that \( \sin (x) \) equals its Maclaurin series for all \( x \). Use the Maclaurin series for \( \sin \left(3 x^{2}\right) \) to evaluate the integral \[ \int_{0}^{0.61} \sin \left(3 x^{2}\right) d x \] Your answer will be an infinite series. Use the first two terms to estimate its value.