I need example in calculus

Mathematics

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Answer

8

Step-by-step solution

3 steps

  1. Displacement is the definite integral of velocity.

    s=∫02v(t) dt=∫023t2 dts = \int_{0}^{2} v(t) \, dt = \int_{0}^{2} 3t^{2} \, dt meters.

  2. Antiderivative formula.

    ∫3t2 dt=t3+C\int 3t^{2} \, dt = t^{3} + C

  3. Evaluate definite integral.

    [t3]02=(2)3−(0)3=8−0=8\left[ t^{3} \right]_{0}^{2} = (2)^{3} - (0)^{3} = 8 - 0 = 8

    The displacement is 8 meters.
    8

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