Double Integration Problem

[SB28210]

Good morning:

I am stuck on integrating this problem:

y over (2 - x) with respect to dy

My attempt was y^2 over 2(2 - x)...but when I plug the limits in I am not getting the correct answer.

I was wondering if anyone can let me know if I am on the right track?

Kind regards,

 

[Deleted member 4993]

Good morning:

I am stuck on integrating this problem:

y over (2 - x) with respect to dy

My attempt was y^2 over 2(2 - x)...but when I plug the limits in I am not getting the correct answer.

I was wondering if anyone can let me know if I am on the right track?

Kind regards,

In your topic heading you are saying double integration - however you are describing single integartion as follows:

\(\displaystyle \int_a^b\frac{y}{2-x}dy\)

Here only variable is 'y' - so you cannot have double integration.

Please post the EXACT original problem.

 

[SB28210]

My apologies:

the exact problem is

Outside is the Integral of x (lower limit of zero...upper limit of One)
Inside is the integral of y (lower limit of zero...upper limit of (2 - X).)

of the function... Y over (2-x)...what you had.

When I integrate with respect to dy I get Y^2 over 2(2-x)..

plugging in the upper limit I get ...

x^2 - 4x +4 over 4-2x (I'm guessing the lower limit is zero)

So I'm sort of stuff integrating this top piece with respect to X

Kind regards.

the correct answer is 3/4

 

[Deleted member 4993]

My apologies:

the exact problem is

Outside is the Integral of x (lower limit of zero...upper limit of One)
Inside is the integral of y (lower limit of zero...upper limit of (2 - X).)

of the function... Y over (2-x)...what you had.

\(\displaystyle \int_0^1\int_0^{2-x}\frac{y}{2-x}dy\, dx \, = \, \frac{1}{2}\int_0^1(2-x)dx\)

Now continue....

When I integrate with respect to dy I get Y^2 over 2(2-x)..

plugging in the upper limit I get ...

x^2 - 4x +4 over 4-2x (I'm guessing - why guess??? - you should calculate and know! the lower limit is zero)

So I'm sort of stuff integrating this top piece with respect to X

Kind regards.

the correct answer is 3/4