A particle travels along a straight line with a velocity of v(t)=3e^(-1/2)sin(2t) meters per second. What is the total distance in meters, traveled by the particle during the time interval 0

Question

A particle travels along a straight line with a velocity of v(t)=3e^(-1/2)sin(2t) meters per second. What is the total distance in meters, traveled by the particle during the time interval 0<t<2 seconds?

anonymous · Answer

$$\int\limits v(t) = s(t) $$ = position function, this is your first step

anonymous · Answer

I have:
$$\int\limits_{0}^{2}3e ^{-t/2}\sin 2t$$
This gives me 1.85 as the answer, but it says the answer is 2.261

anonymous · Answer

do you want gross or net?  total distance (left and right) you'll have to integrate the absolute value of the integrand.

anonymous · Answer

Not sure? That is the exact question.

anonymous · Answer

try doing it with absolute value then...

anonymous · Answer

Neither of the limits of integration is negative though

anonymous · Answer

i just did it... it is absolute value.  2.261

anonymous · Answer

How?

anonymous · Answer

$$\int\limits\limits_{0}^{2} |3e ^{-t/2}\sin 2t| dt$$

anonymous · Answer

I checked and that is correct, but how would I know when to take the absolute value?

anonymous · Answer

Meaning, find where it is negative, and split the integral. You can look at the graph and see that there are negative areas.

anonymous · Answer

Also, your problem calls for TOTAL distance, not just positive distance, or the delta between beginning and ending, so that includes "negative" (read: backwards) distance.

anonymous · Answer

you'll have to pay attention to the wording of the problem...  
total as opposed to net... etc...

anonymous · Answer

Thank you both!