Which of the following expressions represents the total distance traveled (in meters)…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Which of the following expressions represents the total distance traveled (in meters) by a particle with velocity v(t)=t2−4t+3v(t)=t^{2}-4t+3 m/s from t=0t=0 to t=4t=4 seconds? (a) ∣∫04v(t) dt∣\displaystyle \left|\int_{0}^{4} v(t)\,dt\right| (b) ∫01v(t) dt+∫34v(t) dt\displaystyle \int_{0}^{1} v(t)\,dt+\int_{3}^{4} v(t)\,dt (c) ∫04∣v(t)∣ dt\displaystyle \int_{0}^{4} |v(t)|\,dt (d) ∫04v(t) dt\displaystyle \int_{0}^{4} v(t)\,dt

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