← Multivariable Calculus

How to solve

Over a rectangle the double integral splits into two single integrals done one after the other.

Steps

  1. Integrate in x holding y fixed.
  2. Substitute the x-limits.
  3. Integrate the result in y.

Example

∬ 4xy dA over [0, 2] × [0, 3].

  1. Inner: ∫₀² 4xy dx = 8y.
  2. Outer: ∫₀³ 8y dy = 36.

Answer: 36

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