$8-$ Solve the following integration using

${\displaystyle \underset{0\mathrm{.}1}{\overset{0\mathrm{.}4}{}}}2e^{sin}d$

i$)$ A power series for $e^{sin}$ to obtain using Maclaurin series up to three significant figures.

ii$)$ Defined integration method to solve it accurately up to three significant figures.

iii$)$ Find the error between the final values

iv$)$ Evaluate and compare the obtained results of any differences using technically correct language to justify which method is accurate.