Your Task

Clearly, using the Midpoint Method with more than a few rectangles is difficult due to the large number of calculations involved. However, MATLAB can be used

to quickly perform these calculations, even for very large $n.$ In this problem you will define a MATLAB function, midpoint, that accepts four inputs:

a$,$ the left interval endpoint

b$,$ the right interval endpoint

$n,$ the number of rectangles

$f,$ a handle to a numeric MATLAB function$--f$ here is an anonymous function

and returns one output:

A$,$ the area approximated using the Midpoint method.

The function declaration has already been provided in the solution template. Complete the function definition by following the steps below:

Compute the rectangle width, Deltax, using the inputs $a,b,$ and $n$ according to the formula above.

Use the linspace function to generate a vector of $n$ equally spaced points between a and b$,$ midpoints. $($Hint: your interval of the midpoints should

not start and end at a and b$,$ respectively.$)$

Obtain the vector of rectangle heights, heights, by evaluating the input function at midpoints.

Obtain the vevtor of rectangle areas, a reas, by multiplying the rectangle heights by the rectangle width, Deltax.

Sum the vector of rectangle areas using the sum function to obtain the Midpoint Method area estimate, Am$.$

Code has been provided to test your function using the existing code in the Code to Call Your Function Box. As written, it will call midpoint to estimate the

area for $f(x)=x^2$ on $0,1$ for $n=10.$ You are encouraged to call your function for different values of $n$ and to check the corresponding outputs for debugging

purposes. $($Hint: What value should the calculated area approach as $n?)$