# Thread: Areas and Distances, Calculus

1. ## Areas and Distances, Calculus

A particle moves along a straight line with velocity v(t)=t+2 meters/second. Assume that the time t is measured in seconds. Suppose that t[0] .. t[3] divide the interval [2,8] into 3 equal intervals. Use these subintervals and the right endpoints as sample points to compute a Riemann sum which approximates the distance travelled by the particle for the interval of time [2,8].

How do I do this? Everytime I do it I get 98 as an answer

2. Originally Posted by Velvet Love
A particle moves along a straight line with velocity v(t)=t+2 meters/second. Assume that the time t is measured in seconds. Suppose that t[0] .. t[3] divide the interval [2,8] into 3 equal intervals. Use these subintervals and the right endpoints as sample points to compute a Riemann sum which approximates the distance travelled by the particle for the interval of time [2,8].

How do I do this? Everytime I do it I get 98 as an answer
$\Delta t = \frac{8-2}{3} = 2$

$\int_2^8 v(t) \, dt \approx 2[v(4) + v(6) + v(8)] = 2(6 + 8 + 10) = 48$ m