For a differentiable velocity function

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

Problem

For a differentiable velocity function v(t)v(t), which of the following expressions gives the particle’s average velocity on the time interval [a,b][a,b] with a<ba<b? (a) v(b)−v(a)b−a\displaystyle \frac{v(b)-v(a)}{b-a} (b) ∫abv(t) dt\displaystyle \int_{a}^{b} v(t)\,dt (c) 1b−a∫abv(t) dt\displaystyle \frac{1}{b-a}\int_{a}^{b} v(t)\,dt (d) 1b−a∫ab∣v(t)∣ dt\displaystyle \frac{1}{b-a}\int_{a}^{b} |v(t)|\,dt

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