Posted by **Sandy** on Wednesday, March 9, 2011 at 7:46am.

An object moves along the x-axis with a velocity of v(t) = sin(pi/3)t for time t greater than or equal to 0. What is the total distance traveled by the object over the time interval 0 less than or equal to t less than or equal to 4?

- AP Calculus -
**Damon**, Wednesday, March 9, 2011 at 8:19am
well, from t = 0 to t = 3

sin(pi t/3 ) is positive

and

from t = 3 to t = 4, sin (pi t/3) is negative but the distance is still a positive quantity even if movingbackwards

so

integrate from t = 0 to t = 3

sin(pi t/3)dt

then integrate from t = 3 to t = 4

sin (pi t/3) dt

add the absolute values of both

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