# (b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3| v(t) < v O on [4, 6]. Thus, from this equation, the distance traveled is 4 9. |v(t)| dt [-v(t)] dt + v(t) dt 4. 4 9. = | (-?+t + 12) | (? - t - 12) dt dt + 16 ,3 + 12t - 12t 2 + 2 14 82 3

Question

A particle moves along a line so that its velocity at time t is v(t)=t2-t-12. Find the distance traveled during this time period. (Please see the image!) Thank you!!