Compute $R_{6}, L_{6}$, and $M_{3}$ to estimate the distance traveled over $[0,3]$ if the velocity at half- \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline$t(s)$ & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\ \hline$v(\mathrm{~m} / \mathrm{s})$ & 0 & 13 & 18 & 25 & 17 & 14 & 19 \\ \hline \end{tabular} (Give an exact answer. Use symbolic notation and fractions where needed.)

Step 1 ：Calculate R6 using the trapezoidal rule: R6 = 0.5 * ( (v(0) + v(3))/2 + v(0.5) + v(1) + v(1.5) + v(2) + v(2.5) )

Step 2 ：Substitute the given values: R6 = 0.5 * ( (0 + 19)/2 + 13 + 18 + 25 + 17 + 14 )

Step 3 ：Simplify: R6 = 0.5 * ( 19/2 + 87 ) = 0.5 * 125/2 = 125/4 = 31.25

Step 4 ：Calculate L6 using the trapezoidal rule: L6 = 0.5 * ( v(0) + v(0.5) + v(1) + v(1.5) + v(2) + v(2.5) + v(3) )

Step 5 ：Substitute the given values: L6 = 0.5 * ( 0 + 13 + 18 + 25 + 17 + 14 + 19 )

Step 6 ：Simplify: L6 = 0.5 * 106 = 53

Step 7 ：Calculate M3: M3 = v(1) = 18

Step 8 ：The estimated distance traveled over [0,3] is approximately 31.25 meters using the trapezoidal rule.