iterated integral

A double integral computed as two nested single-variable integrals, one variable integrated at a time.

An iterated integral computes a double integral by treating the outer variable as a constant while integrating with respect to the inner one: $\int_c^d f(x,y)\,dy$ integrates with respect to $y$ while $x$ sits frozen, producing a function of $x$ alone, which the outer integral then integrates over $[a,b]$ . Getting the two steps backwards is the most common setup error, not an arithmetic one.

Examples

$\int_0^2\!\int_0^1 xy^2\,dy\,dx$ : the inner integral gives $\tfrac{x}{3}$ , and the outer integral then gives $\tfrac23$ .