Evaluate the integral $\iint _ { R } \frac { x + y } { x - y } d A$ , where R is the triangular region with vertices (1, 0), (0, -1), and (0, 0).
A)0
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 3 } { 4 }$
E)1
F) $\frac { 3 } { 2 }$
G)2
H)-2

Question

Evaluate the integral $\iint _ { R } \frac { x + y } { x - y } d A$ , where R is the triangular region with vertices (1, 0), (0, -1), and (0, 0).
A)0
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 2 }$ 
D) $\frac { 3 } { 4 }$ 
E)1
F) $\frac { 3 } { 2 }$ 
G)2
H)-2

Quizplus · Accepted Answer

The integral simplifies due to the symmetry of the function over the triangular region. The region is symmetric about the line y = -x, and the integrand function $\frac{x+y}{x-y}$ changes sign when x and y are swapped, making the integral over the symmetric region equal to zero.

Evaluate the Integral ∬Rx+yx−ydA\iint _ { R } \frac { x + y } { x - y } d A∬R​x−yx+y​dA

Evaluate the Integral $\iint _ { R } \frac { x + y } { x - y } d A$