Math Q

[JJChicken]

Don't need to give me the answer, but perhaps point me in the right direction. How to integrate f(x,y) over its domain (all real x, y) such that x + y < 0.5?

Kinda stumped cause the values of y depend on x, so dunno how to integrate y out first.

Thanks resident ATOT geniuses!

 

[Spikesoldier]

midterm tomorrow morning?

 

[Born2bwire]

Ummmm...

x+y < 0.5
x < 0.5 - y
....

Wait...

What do you mean you do not know how to integrate y first?

 

[JJChicken]

Is it possible to take in my terminal values for y, 0 and 0.5 - x?

 

[JJChicken]

Ummmm...

x+y < 0.5
x < 0.5 - y
....

Wait...

What do you mean you do not know how to integrate y first?

Doing an integration over two variables - so integrate y first then integrate x

 

[JJChicken]

On my iPhone, so bit hard to write this.

Say I want to integrate f(x,y)=xy where 0<x<1, 0<y<1, x + y < 0.5

So straight away, I know x < 0.5 and y < 0.5. What I did next was integrate y, holding x constant and over 0 to 0.5-x. Since I'm taking x constant, I thought its okay to do this. This leaves me the expression x(0.5-x)^2/2. I then integrate x over 0 to 0.5. Is this correct?

Thanks

 

[Newbian]

The answer is 42.

 

[DrPizza]

You said all real (x,y), now it's all positive reals (x,y)? What's the domain??

 

[Farmer]

Your question is, "what are the limits of integration for the double integral"

Your previous post might be right, but here it is anyway.

Your boundary is a straight line in the x-y space (y = -x + 0.5 is the equation of that line). There are lots of ways to do this. Most intuitive way (may not be easiest depending on what f(x,y) is):

Let the x integral be the outer integral, and the y integral the inner integral.

If it's all positive (x,y) instead of all (x,y), then the lower limit in integration in both cases is 0, not -Inf.

 

[JJChicken]

You said all real (x,y), now it's all positive reals (x,y)? What's the domain??

yeah sorry, the domain should 0<x<1, 0<y<1

 

[JJChicken]

Your question is, "what are the limits of integration for the double integral"

Your previous post might be right, but here it is anyway.

Your boundary is a straight line in the x-y space (y = -x + 0.5 is the equation of that line). There are lots of ways to do this. Most intuitive way (may not be easiest depending on what f(x,y) is):

Let the x integral be the outer integral, and the y integral the inner integral.

If it's all positive (x,y) instead of all (x,y), then the lower limit in integration in both cases is 0, not -Inf.

Dude, thanks so much.

 

[Farmer]

Dude, thanks so much.

Hey, it's more interesting than work.

 

[MegaVovaN]

Farmer wins this thread.