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Planar motion (with integrals)

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Problem

A particle moving in the x, y-plane has velocity vector given by v, left parenthesis, t, right parenthesis, equals, left parenthesis, minus, 2, e, start superscript, t, end superscript, comma, e, start superscript, t, end superscript, right parenthesis for time t, is greater than or equal to, 0.
What is the magnitude of the displacement of the particle between time t, equals, 2 and t, equals, 3?
Round to the nearest tenth.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
units
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