Solve the problem.
-Write
$$\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { y } f ( x , y ) d x d y + \int _ { 2 } ^ { 4 } \int _ { 0 } ^ { 4 - y } f ( x , y ) d x d y$$
as a single iterated integral.
A) $\int _ { 0 } ^ { 2 } \int _ { 2 } ^ { 4 - x } f ( x , y ) d y d x$
B) $\int _ { - 2 } ^ { 2 } \int _ { x } ^ { 4 - x } f ( x , y ) d y d x$
C) $\int _ { - 2 } ^ { 2 } \int _ { 2 } ^ { 4 - x } f ( x , y ) d y d x$
D) $\int _ { 0 } ^ { 2 } \int _ { x } ^ { 4 - x } f ( x , y ) d y d x$

Question

Quizplus · Accepted Answer

The region of integration can be described as the triangle bounded by the lines $y=0$, $y=2$, and $x=2$, and the triangle bounded by the lines $y=0$, $y=4-x$, and $x=2$. Therefore, the integral can be written as: $$\int_{0}^{2}\int_{x}^{4-x}f(x,y)dydx.$$

Solve the Problem ∫02∫0yf(x,y)dxdy+∫24∫04−yf(x,y)dxdy\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { y } f ( x , y ) d x d y + \int _ { 2 } ^ { 4 } \int _ { 0 } ^ { 4 - y } f ( x , y ) d x d y∫02​∫0y​f(x,y)dxdy+∫24​∫04−y​f(x,y)dxdy

Solve the Problem $\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { y } f ( x , y ) d x d y + \int _ { 2 } ^ { 4 } \int _ { 0 } ^ { 4 - y } f ( x , y ) d x d y$