Problem $2$

$[15$ points$]$ Consider the integral

$\backslash$int$\_0^1(1000)/(\backslash$sqrt$($x$+0\mathrm{.}01))$dx

$($a$)$ Numerically evaluate this integral using the trapezoidal rule with n subintervals of uniform

length h$.$ Make a log$-$log plot of the relative error $|$I$\_($exact $)-$I$\_($numerical $)(|)/($I$\_($exact $))$ vs n and discuss

the accuracy of the method. Take n$=8,16,32,$dots Include enough values of n such that the

overall scaling of the error for large n is clear $($at the right side of the graph, the error should

be a straight line downward$).$

$($b$)$ Repeat part $($a$)$ using Simpson's rule.

SEE PHOTO bc it didnt translate right