Question

Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by

v(t) = 525,600(0.42t2 + 2.7t − 1) hours of video per year (0.5 ≤ t ≤ 7),
where t is time in years since the start of 2005.†

(a) Find an expression for the total number of hours

V(t) of video at time t
(starting from zero hours of video at t = 0.5).

V(t) =