= Iterated integral
{title2=$\int_a^b\left(\int_{c(y)}^{d(y)}f(x,y)\,dx\right)dy$}
An <iterated integral> performs successive one-variable <integrals>. In the displayed expression, $y$ is held fixed during the inner <integration> over $x$, and the result is then integrated over $y$. The inner bounds may depend on that fixed outer variable. By contrast, an inner bound depending on an already integrated variable does not specify such a nested operation without further interpretation. For example, the <triangle> $0\leq y\leq1$, $2y\leq x\leq2$ gives $\int_0^1\int_{2y}^2f(x,y)\,dx\,dy$, or, in the other order, $\int_0^2\int_0^{x/2}f(x,y)\,dy\,dx$. <Fubini's theorem> and <Tonelli's theorem> supply conditions under which these iterated expressions equal the same <multiple integral>.
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