Question

(1 point) Your velocity is given by v(t)=2t2+8 in m/sec, with t in seconds. Estimate the distance, s, traveled between t=0 and t=8. Use the average of the left and right sums with 4 subdivisions.

Answer 1

Answer:

The estimated distance is 405 meter.

Step-by-step explanation:

Given : Your velocity is given by $v(t)=2t^2+8$ in m/sec, with t in seconds.

To find : Estimate the distance, s, traveled between t=0 and t=8 ?

Solution :

We have to integrate the function from 0 to 8 to get the distance.

Integrate $v(t)=2t^2+8$ w.r.t  t,

$\int\limits^8_0 {2t^2+8} \, dt$

We know, $\int\limits {x} \, dx=\frac{x^2}{2}$

$=[\frac{2t^3}{3}+8t]^8_0$

$=(\frac{2(8)^3}{3}+8(8))-(\frac{2(0)^3}{3}+8(0))$

$=(\frac{1024}{3}+64)-(\frac{0}{3}+8(0))$

$=\frac{1024+192}{3}$

$=\frac{1216}{3}$

$=405.33$

The estimated distance is 405 meter.