For a particle moving along a straight line with velocity

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For a particle moving along a straight line with velocity v(t)v(t), which of the following definite integrals gives the particle’s total distance traveled from t=at=a to t=bt=b? (a) ∣∫abv(t) dt∣\displaystyle \left|\int_{a}^{b} v(t)\,dt\right| (b) ∫abv(t) dt\displaystyle \int_{a}^{b} v(t)\,dt (c) ∫abv′(t) dt\displaystyle \int_{a}^{b} v'(t)\,dt (d) ∫ab∣v(t)∣ dt\displaystyle \int_{a}^{b} |v(t)|\,dt

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