Due: Friday, March $8,2024,11$:$59$ PM

Write a program to evaluate the following integral between a and $b.$ Use the trapezoidal approximation to

evaluate the integral. The program should prompt the user to enter the parameter $m,$ the lower limit $a,$

upper limit $b,$ and the number of trapezoids $n.$ The range of the parameter must be $\underset{x0}{lim}\frac{sin(mx)}{mx}=1{\displaystyle \underset{a}{\overset{b}{}}}\frac{sin(mx)}{mx}dx$ Area ~$=\frac{b-a}{2n}[g(x_0)+2g(x_1)+$cdots$+2g(x_{n-1})+g(x_n)]$

$x_k=a+k\frac{b-a}{n},k=0,1,$dots,$n$

$g(x)=\frac{sin(mx)}{mx}0.$ The program

should continue $to$ prompt the user and calculate integrals until the number $of$ trapezoids entered $is$ zero.

The program should take into account the possibility $of$ incorrect input from the user. Note that

$\underset{x0}{lim}\frac{sin(mx)}{mx}=1$ using L'Hopital's rule.

${\displaystyle \underset{a}{\overset{b}{}}}\frac{sin(mx)}{mx}dx$

The integral can $be$ approximated using the trapezoidal rule:

Area ~$=\frac{b-a}{2n}[g(x_0)+2g(x_1)+$cdots$+2g(x_{n-1})+g(x_n)]$

$x_k=a+k\frac{b-a}{n},k=0,1,$dots,$n$

$g(x)=\frac{sin(mx)}{mx}$