MHB Solution to Double Integral Problem

[TheArun]

I want the answer for this and how is it solved.
double integral(x²+y² dxdy) over the region in pos quadrant for which x+y<=1.

 

[chisigma]

Re: iam new...i have a question...pls help.

I want the answer for this and how is it solved.
double integral(x²+y² dxdy) over the region in pos quadrant for which x+y<=1.

Wellcome on MHB Arun!...

... did You make some attempt?...

Kind regards

$\chi$ $\sigma$

 

[TheArun]

Re: iam new...i have a question...pls help.

ya...sure..tried many times...iam getting 2/3 as ans...but accd to text it is 1/6...dont know y iam wrong.
Btw thank for reply.

 

[Jameson]

Re: iam new...i have a question...pls help.

ya...sure..tried many times...iam getting 2/3 as ans...but accd to text it is 1/6...dont know y iam wrong.
Btw thank for reply.

Hi Arun,

Welcome to MHB! :) Please use proper English here, meaning don't use lots of abbreviations like "ans" for "answer".

In order to help you we need to see what work you've done, so without seeing how you got $\frac{2}{3}$ we don't know where you went wrong.

Jameson

 

[TheArun]

Re: iam new...i have a question...pls help.

Hi Arun,

Welcome to MHB! :) Please use proper English here, meaning don't use lots of abbreviations like "ans" for "answer".

In order to help you we need to see what work you've done, so without seeing how you got $\frac{2}{3}$ we don't know where you went wrong.

Jameson

sorry fed up with all the subscripts and superscripts...is der some easier way...anyway i have done it in word.but it is showing invalid file.

 

[Jameson]

Re: iam new...i have a question...pls help.

sorry fed up with all the subscripts and superscripts...is der some easier way...anyway i have done it in word.but it is showing invalid file.

We use Latex on MHB and have a http://www.mathhelpboards.com/f26/ that explains how to use it. Until you learn how to use Latex I suggest taking a screenshot of your work and uploading the image to TinyPic. Then you can post the picture here.

Here is an example of what $\LaTeX$ can do:

$$\int_0^{\infty}e^{-x^2}\,dx=\frac{\sqrt{\pi}}{2}$$

 

[TheArun]

Re: iam new...i have a question...pls help.

We use Latex on MHB and have a http://www.mathhelpboards.com/f26/ that explains how to use it. Until you learn how to use Latex I suggest taking a screenshot of your work and uploading the image to TinyPic. Then you can post the picture here.

Here is an example of what $\LaTeX$ can do:

$$\int_0^{\infty}e^{-x^2}\,dx=\frac{\sqrt{\pi}}{2}$$

this is the image

 

[chisigma]

All right!... the region of integration is the 'colored area' of the figure...

http://www.123homepage.it/u/i69735807._szw380h285_.jpg.jfif

The symmetry respect to x and y is evident, so that we can choose one or the other order of integration and write...

$\displaystyle \int\int_{A} (x^{2} + y^{2})\ dy\ dx = \int_{0}^{1} dx\ \int_{0}^{1-x} (x^{2}+y^{2})\ dy = \int_{0}^{1} |x^{2}\ y + \frac{y^{3}}{3}|_{0}^{1-x}\ dx = \int_{0}^{1} (\frac{1}{3} - x + 2\ x^{2} - \frac{x^{3}}{3})\ dx$ (1)

Now are You able to proceed?...

Kind regards

$\chi$ $\sigma$

 

[TheArun]

so it turns out to be 5/12 right...?
But answer in a text is shown to be 1/6...author's mistake is it?
And i would also like to know y u chose this order of integration is it easier this way...the logic?
A very big thanks.

 

[Petrus]

so it turns out to be 5/12 right...?
But answer in a text is shown to be 1/6...author's mistake is it?
And i would also like to know y u chose this order of integration is it easier this way...the logic?
A very big thanks.

Hello Arun,
I get it also to $$\frac{5}{12}$$ and about the order of integration both is same difficult/simple. You can try it out if you want.
edit: When you mean 'order of integration' I asume you mean why he did choose $$1-x$$ insted of $$1-y$$

Regards,
$$|\pi\rangle$$