Riemann Sums: Videos & Practice Problems

A particle moves along a straight line with velocity, in $m/s$, given by $v\left(t\right)=2t^2+4$, for $t$ in $[1,5]$. Divide the interval $[1,5]$ into $4$ equal subintervals: $[1,2]$, $[2,3]$, $[3,4]$, and $[4,5]$. On each subinterval, assume that the particle’s velocity remains constant at the value of $v\left(t\right)$ evaluated at the midpoint of the subinterval. Using these constant‐velocity subintervals, approximate the displacement of the particle on $[1,5]$.