Approximating Definite Integrals — Question 9

Question 9 – Solution

Step 1: Find the time width. $$h=\frac{4-0}{4}=1\text{ second}.$$ Step 2: Apply the trapezoidal formula. $$\begin{align*} T_4&=\frac h2[v_0+2v_1+2v_2+2v_3+v_4]\\ &=\frac12[0+2(3)+2(5)+2(6)+4]\\ &=\frac12[0+6+10+12+4]\\ &=\frac12(32)=16. \end{align*}$$ Step 3: Include units. Velocity times time gives displacement in meters. $$\boxed{16\text{ m}}$$