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.

  • 2 variables
  • 2 worked examples
  • 14 in Applications of Integrals

Variables

Variables used in the Work (General) formula
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

1 more worked examplePremium

Find the work done by F(x) = 1/x² N moving an object from x = 1 m to x = 4 m.

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Common questions

What is the Work (General)?

Work done by a variable force F(x) over a displacement from a to b. It is one of the applications of integrals formulas in the CalcRef reference.

What do the symbols in the Work (General) mean?

In the Work (General), a is the start position (m); b is the end position (m).

How do you use the Work (General)?

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

Practice

Quiz yourself on Applications of Integrals

Work (General) is one of 14 Applications of Integrals formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.