Trapezoidal challenge. In this problem we will create a function called trapint that has the following format: s $=$ trapint$($f$,$ I$),$ where f is a n $1$ column vector of samples of a function f on an n$-$point equispaced grid over the interval I, and

$.$ So$,$ for example, if n $=100$ and I $=[$a$,$b$],$ then

where x$1=$ a $<$ x$2<$ x$3<,$x$99<$ x$100=$ b are equally$-$spaced points along the interval $[$a$,$b$].$

To get started, open a new script and set it up so that it is a function of the form s $=$ trapint$($f$,$ I$).$ Here, f will be a length n vector of values just like f above. The interval I will be a $2$ row vector containing the interval endpoints a and b$.$

$($a$)$ Write down the trapezoidal rule with respect to the values fj $=$ f$($xj$),$ j $=1,2,,$n$.$ You should notice it requires a quantity called $$x$.$ Using just the input to the function trapint, describe how to compute $$x$.$

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