Applications of Integrals · Work & Force

Work (General)

W=abF(x)dxW = \int_a^b F(x)\, dx

Work done by a variable force F(x) over a displacement from a to b.

Variables

SymbolNameUnit
aStart positionm
bEnd positionm

Worked examples

Find the work done by F(x) = 3x² N over [0, 2] m.
  1. W = ∫₀² 3x² dx = [x³]₀² = 8 J

Answer: 8 J

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