I would really appreciate some help with the following:
The velocity function is v(t)= -t^2 +6t -8. Find the distance traveled during the time interval [0,6].
I know that the formula for distance traveled = |v(t)|*dt on the given time interval [a,b], so my formula would be |-t^2+6t-8| where a=0 and b=6.
I calculated the anti-derivate of v(t) to be -(t^3)/3 +3t^2 -8t.
I was able to calculate the displacement to be -12, but I don't think that has any relevance to this particular problem?
At this point, I'm absolutely stuck. Any explanations of the process of this computation would be very greatly appreciated.