Andrew F. answered • 12/17/21
Experienced private school teacher
Natasha, there is the "cheating way" and the way you are probably being asked to do this.
The key is to separate when the particle moves left vs right--you will find the distance moved left and add that to the distance moved right during the given interval.
v(t)= (-1)(t2 + t - 2)
v(t)=(-1) (t + 2)(t - 1)
you should see that v(t) is negative for 1 < t < 2
amd v(t) is positive for 0 < t < 1
now you can find the distance travelled for each interval by integration of each interval separately, making sure to have each distance be positive
By the way, the "cheating way" is integrate the absolute value of the velocity function--TI-84 does this easily
Hope this helps--Andrew
Andrew F.
hard to type this, but I'll try: Math9 brings up the definite integral then enter your time interval for the limits of integration then "MATH-NUM-1" brings up absolute value, then enter the function (use x for variable) then dx closes the definite integral try it and let me know what you get12/17/21
Natasha W.
I got 3 lol. I'm going to try it, but you explained it very well. Thank you! I got it right! Thanks so much12/17/21
Andrew F.
brava! You should get 3 both ways, so the calculator is a good way to check your work12/17/21
Natasha W.
How can you do this with the Ti-84?12/17/21