For a particle moving along a line with continuous velocity

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

Problem

For a particle moving along a line with continuous velocity v(t)v(t), which of the following definite integrals gives the particle’s net displacement from t=at=a to t=bt=b? (a) ∫ab∣v(t)∣ dt\displaystyle \int_a^b |v(t)|\,dt (b) ∣∫abv(t) dt∣\displaystyle \left|\int_a^b v(t)\,dt\right| (c) ∫abv(t) dt\displaystyle \int_a^b v(t)\,dt (d) ∫bav(t) dt\displaystyle \int_b^a v(t)\,dt

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