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Calculate work required to move a particle

by RoRi

Given a force described by the function

    \[ f(x) = 3x^2 + 4x \]

moving a particle along the x-axis. Calculate the following:

  1. The Joules of work done moving the particle from x = 0 to x = 7.
  2. The Joules of work done moving the particle from x = 2 to x = 7.
  1. We use the formula for work to compute,

        \[ W = \int_0^7 (3x^2 + 4x) \, dx = x^3 \biggr \rvert_0^7 + 2x^2 \biggr \rvert_0^7 = 343 + 98 = 441 \text{ Joules}. \]

  2. We use the formula for for work to compute,

        \[ W = \int_2^7 (3x^2 + 4x) \, dx = (x^3 + 2x^2) \biggr \rvert_2^7 = 441 - 16 = 425 \text{ Joules}.\]

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