Iterated Integrals and Fubini's Theorem

A double integral generalizes the concept of a single-variable integral to functions of two variables, enabling the computation of the volume beneath a surface z = f(x, y) over a planar region R . For a rectangular region defined by a ≤ x ≤ b and c ≤ y ≤ d, and for func...

A double integral finds the total accumulation of a function over a region. It is evaluated using an iterated integral, which expresses the double integral as two single integrals.

For a function over a rectangle in the xy-plane, holding x constant means slicing the region perpendicular to the x-axis and integrating with resp...