HOMEWORK $20$: Numerical Integration of Plecewise Functions. $($VBA$)$

You have already written a UDF that, for a given $x-$value, calculates the value of $f(x)$ where $f(x)$ is the following piecewise function.

$f(x)=\{\begin{array}{cc}-x^2-6x-2\mathrm{.}5,& x0\\ -1\mathrm{.}5-3^{0\mathrm{.}1x},& 0=10\end{array}$

Graphing the function from ${\displaystyle \underset{-5}{\overset{15}{}}}f(x)dx-5$ cave $ue$ tha fallauxinn $im...$

Write a numerical integration function that integrates this piecewise function from $-5to15.$ Use $1,000$ steps $to$ approximate the integral. That $isto$ say, find:

${\displaystyle \underset{-5}{\overset{15}{}}}f(x)dx$

What $is$ the approximate value $of$ the integral using a right$-$side integration?

$[student$ response$]$

What $is$ the approximate value $of$ the integral using a left$-$side integration?

$[student$ response$]$

What $is$ the approximate value $of$ the integral using a midpoint integration?