From Example 6.7.1, $\mathrm{\λ}\=5.078061188$, and rounded to four decimal places, $\mathrm{\λ}$ becomes $\stackrel{\^}{\mathrm{\λ}}\=5.0781$. By trial-and-error, the smallest value of $n$ in the Trapezoid rule for which the approximation to the integral rounds to $\stackrel{\^}{\mathrm{\λ}}$ is $n\=312$. The Trapezoid rule with this partition returns $5.078050007$, which rounds up to $\stackrel{\^}{\mathrm{\λ}}\=5.0781$.

The  tutor could be used to implement the Trapezoid rule for different values of the partition $n$. Alternatively, the ApproximateInt command can be use, as in Table 6.7.2(a).

At $n\=311$, the Trapezoid rule yields $5.078049935$, which rounds to $5.0780$. On the other hand, at $n\=312$, the Trapezoid rule yields $5.078050007$, which rounds to $5.0781\=\stackrel{\^}{\mathrm{\λ}}$.