Solve the problem.
-Write
$$\int _ { 0 } ^ { 9 } \int _ { 0 } ^ { y } f ( x , y ) d x d y + \int _ { 9 } ^ { 18 } \int _ { 0 } ^ { 18 - y } f ( x , y ) d x d y + \int _ { 0 } ^ { 9 } \int _ { y } ^ { 9 } f ( x , y ) d x d y + \int _ { 0 } ^ { 9 } \int _ { 9 } ^ { 18 - y } f ( x , y ) d x d y$$
as a single iterated integral with the order of integration reversed.
A) $\int _ { 0 } ^ { 18 } \int _ { 9 } ^ { 18 - x } f ( x , y ) d y d x$
B) $\int _ { 9 } ^ { 18 } \int _ { 0 } ^ { 18 - x } f ( x , y ) d y d x$
C) $\int _ { 0 } ^ { 18 } \int _ { 0 } ^ { 18 - x } f ( x , y ) d y d x$
D) $\int _ { 9 } ^ { 18 } \int _ { 9 } ^ { 18 - x } f ( x , y ) d y d x$

Question

Quizplus · Accepted Answer

The given integrals cover the entire square region from (0,0) to (9,9) and a triangular region from (9,0) to (18,0) to (9,9). When reversing the order of integration, the entire region from x=0 to x=18 and y=0 to y=18-x is covered, which matches option C.

Solve the Problem As a Single Iterated Integral with the Order of Integration