If R is the triangle bounded by x+y = 1, x = 0, y =0, evaluate the double integral over R...

Question

If R is the triangle bounded by x+y = 1, x = 0, y =0, evaluate the double integral over R ofcos((x+y)/(x-y)) dx dyby changing variables. Leave your answer in terms of sin(1).

Baljit · Accepted Answer

We have to calculate following double integral.
Here R is triangular region bounded by x+y=1,x=0,y=0
Now by change of variable method we will put  u=x+y and v= x-y
so  x=(u+v)/2  and  y=(u-v)/2
Now  point(x,y) varies in triangular region R, So let’s  suppose  point(u,v) varies in region  P
Now x+y=1, y=0,

If R is the triangle bounded by x+y = 1, x = 0, y =0, evaluate the double integral over R of cos((x+y)/(x-y)) dx dy by changing variables. Leave your answer in terms of sin(1).

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