Calculate the volume under a surface over a rectangular region in 3D space.
Function Definition
Integration Bounds
X Limits
Y Limits
Geometry
Calculating the volume over the rectangle [ 0, 1 ] × [ 0, 2 ] in the xy-plane.
Integration Result
1
Volume / Integral Value
Region Area2
Samples2500 pts
Iteration TypeRectangular
About this calculator
What is a Double Integral?
A double integral is the extension of the definite integral to multivariable functions. While a single integral finds the area under a curve, a double integral finds the volume under a surface f(x, y) over a defined region R in the xy-plane.
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Pro Tips
For rectangular regions, the order of integration (dx dy or dy dx) usually doesn't change the result.
If f(x, y) = 1, the double integral simply gives you the area of region R.
Double integrals are used for finding mass, center of gravity, and electric charge distribution.
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Fun Facts
"Fubini's Theorem states when a double integral can be computed as an iterated integral."
"In probability, double integrals are used with joint probability density functions."
"Triple integrals extending this concept into 4D space are used to find mass from density in 3D objects."
