Solving Calc AP Problem 1: Total Distance 0-2

[tandoorichicken]

Problem: A particle moves along the x-axis so that any time t >_ 0 its velocity is given by v(t) = ln(t + 1) - 2t + 1. What is the total distance traveled by the particle from t=0 to t=2?

Am I correct that the total distance is the area under the curve? I tried doing the integration on my calculator, and it gave me a negative answer. Then I graphed to make sure I didn't do anything wrong. I don't think I should be getting a negative answer, so... help please.

 

[Math Is Hard]

I think the problem here is that your particle isn't always moving forward. When you measure total distance, you'll need to determine the intervals where the particle is moving backward (where velocity is negative) and take the absolute value of that distance.
Just a thought.

 

[himanshu121]

If it is velocity then area under the curve gives u displacement not distance for calculating distance apply the following formula

Distance covered from time t=a to t=b is

$$\int_a^{b} |v(t)|dt$$

Or draw the graph of |v(t)| from the graph of v(t)

Area under |v(t)| will give u distance