The algorithm shown below estimates the value of

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$

using the composite trapezoid rule with $n$ equally or unequally spaced base points $(x_i,y_i)$

BEGIN

INPUT $x_i,y_i,n$

sum $=0$

DOFOR $i=1,n-1$

${\displaystyle \underset{?}{\overset{?}{}}}={\displaystyle \underset{?}{\overset{?}{}}}+(x_{i+1}-x_i)\frac{y_{i+1}+y_i}{2}$

ENDDO

OUTPUT sum

END

a$)$ Represent the algorithm as a flow chart.

b$)$ Write a Matlab function program TrapRule $(x,y,n)$ which implements this algorithm and

returns the estimated value of the integral to the calling program.

c$)$ Write a Matlab program which calls the function program developed in part $($b$)$ to evaluate the

integral

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}xcos(x)dx$

using $4$ equally spaced base points and prints the result.