Mathematics · University
A separable double integral · formula reference
The rectangular region allows two independent single-variable integrations.
Formula
The rectangular region allows two independent single-variable integrations.
∫₀ᵃ∫₀ᵇ kxy dy dx = ka²b²/4
Worked example
Integrate 9xy over the rectangle 0 ≤ x ≤ 1, 0 ≤ y ≤ 3. Round the final result to 4 decimal places if needed.
Integrate y first to get 9x(3²/2), then integrate x over [0,1].
20.25
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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