Define f(x,y) and integration bounds

∫ba ∫dc f(x,y) dy dx

Function f(x, y)

Operators: + - * / ^ | Functions: sin cos tan exp sqrt log abs | Constants: PI E

Try:

x — Lower Bound (a)

x — Upper Bound (b)

y — Lower Bound (c)

y — Upper Bound (d)

Precision (Gauss-Legendre points per axis)

Function Heatmap f(x,y)

Min

Max

x → right, y → up

Double Integral

—

∬ f(x,y) dx dy

|Result| Magnitude

—

absolute value

Region Area

—

(b−a) × (d−c)

Average Value f̄

—

∬f ÷ Area

Rectangular Region

∬f dA = ∫ₐᵇ ∫꜀ᵈ f(x,y) dy dx

Fubini's Theorem

Order of integration can be swapped

Area of Region

A = (b−a)(d−c)

Average Value

f̄ = (1/A) × ∬f dA

Double Integral Calculator