Is $\iint f(x,y)\; dx\;dy$ called an iterated integral or iterated integrals

Question

In my Calculus 4 class we are learning about finding double and triple integrals. For example, one finds a double integral $$ \iint_E f(x,y)\;dA $$ by writing it as $$ \int_a^b\int_c^d f(x,y)\; dx\;dy $$ Is this call an iterated integral or is it iterated integrals? (So plural or singular.)

Answer 1

An excerpt from the text

Stewart -- Calculus - Early Transcendentals, 6th Ed (2008)

" . . . in this section we see how to express a double integral as an iterated integral, which can then be evaluated by calculating two single integrals."

Answer 2

On my course that I'm creating at the minute, I usually refer to them as double or triple integrals, i.e

• Double Integral $$\iint_R dA$$
• Triple (Volume) Integral $$\iiint_V dV$$

That way, it's easier to understand, it won't scare the crap out of your students. Otherwise I'd call it an iterated integral, since it's one big integral with several parts that is. Hope this helps!