Based on what is learned in class about the left$-$Riemann sum algorithm, construct a MATLAB

function $($numerical solver$)$ that performs the numerical integration using the right Riemann

sum. The formula $($algorithm$)$ for the composite right Riemann sum for a set of $+1$ equally

spaced data points $($or discretized domain points$)$ is:

$=()$

$$

$$

$\backslash$cong $()$

$+1$

$=2$

This numerical solver has the following input$/$output structure:

function $[$I$]=$ frmrsum$($fun$,$a$,$b$,$N$)$

where fun is an anonymous function and x is a vector of the values for the discretized domain. Note

that $=+1$ is the step size of the subinterval between $$ and $+1.$

Critical thinking: Follow the example discussed in class for the left Riemann sum. Both the left and

right Riemann sums represent numerical algorithms, which when coded properly, can be used to

perform numerical integration of functions that cannot be evaluated analytically.

The key is to understand that functions are $$blind$$ to their input variables $($the input variables could

also include functions as in this case$).$ In other words, while the output results depend on the inputs, the

algorithms are independent of the inputs.

Learn how $($and why$)$ to define inputs for functions and how to perform the summation in this

algorithm using the MATLAB function sum instead of a for$-$loop to understand and appreciate the

simplicity and intuitiveness of MATLAB programming.

Instructor: Professor C$.$ A$.$ Tan Copyrighted Materials Lab$-$Homework $01$

ME$2500$: Numerical Methods Using MATLAB Winter $2024$ Term

Lab$-$HW$01$ In$-$Lab and Post$-$Lab Page $11$ of $11$

b$)$ The force per unit length $$ that is exerted by the wind

on a $26$ ft tall sail as a function of its height $$ is given by:

$=175$

$+5/9$ lb$/$ft

The total force F on the sail is calculated by:

$=$

$26$

$0$

Estimate the total force by applying the right Riemann sum with $10$ subintervals $(=10).$

Compare your result with that obtained by the MATLAB built$-$in function integral. Assume that

the result from applying the function integral is exact, what is the relative percentage error in

using the Riemann sum with $10$ subintervals?

c$)$ Increase $$ to $50,$ what is the relative percentage of error? Plot the relative percentage error as a

function of $$ up to $100$