Thread: Bit Stuck on double integral when area is in all four quadrants

1. Bit Stuck on double integral when area is in all four quadrants

So im doing a double integral question, i will avoid posting whole question as is kinda wordy but essentialy:

z=((x-y)^2)/4

and both x and y are defined in the region of a square (+/- 1,+/-1)

i am a little unsure what to set bounds of the integrals as i dont know if the minuses will affect the value. do i just set up the double integral with bound (+1,-1) or is there something more complicated.

Any help will be greatly appreciated, many thanks.

2. Re: Bit Stuck on double integral when area is in all four quadrants

It would help if we knew exactly what you were doing but it sounds like you should just set the limits of integration to cover the entire area that x and y are defined over.

3. Re: Bit Stuck on double integral when area is in all four quadrants

thanks for the reply. This is the full question:

A partially silvered mirror covers the square area with vertices at (±1, ±1). The
fraction of incident light which it reflects at (x, y) is (x − y)
2/4. Assuming a
uniform intensity of incident light, find the fraction reflected.

4. Re: Bit Stuck on double integral when area is in all four quadrants Originally Posted by jakmo1423 thanks for the reply. This is the full question:

A partially silvered mirror covers the square area with vertices at (±1, ±1). The
fraction of incident light which it reflects at (x, y) is (x − y)
2/4. Assuming a
uniform intensity of incident light, find the fraction reflected.
yeah, integrate over all x and y

5. Re: Bit Stuck on double integral when area is in all four quadrants

ok thats great thank you very much 