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AP Calculus

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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 -

    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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