Consider the estimation $of$ the integral ${\displaystyle \underset{0}{\overset{0\mathrm{.}5}{}}}f(x)dx$ where $f(x)is$ shown below.

$ah=0\mathrm{.}1$

$bh=0\mathrm{.}1,$ use a combination $of$ Simpson's $\frac{1}{3}$ rule and trapezoidal rule $to$

obtain the most accurate estimate $of$ the integral's true value $(carefully$ think $of$ the

range where you would use each method$).$ Explain why you could not use just Simpson's

$\frac{1}{3}$ rule.