Change of variables in double integral with u = x² + y²

[BvU]

You answer the question

what $\ x\over \sqrt{x^2 + y^2}$represents

 

[chetzread]

You answer the question

it has no meaning , right ? the author just simply put inside the equation, right ?

 

[BvU]

You think I annoy you with so many questions when there is no meaning ? What is the sine of the red angle ? What is the cosine ?

 

[chetzread]

You think I annoy you with so many questions when there is no meaning ? What is the sine of the red angle ? What is the cosine ?
View attachment 105794

You answer the question

It's cos theta, so?

 

[Ray Vickson]

It's cos theta, so?

What do you think?

 

[Mark44]

@chetzread, I believe that BvU's hint is not about merely switching the order of integration (i.e., dxdy vs. dydx), but instead, about changing to a polar integral. This problem quite a bit easier if you do it this way.

 

[BvU]

It's cos theta, so?

So ? Wouldn't substituting $\theta$ as integration variable be a sensible thing to try ?

 

[chetzread]

So ? Wouldn't substituting $\theta$ as integration variable be a sensible thing to try ?

ok, i got the ans now ...I'm wondering is this a special case? I have never learned and see this before ...

 

[BvU]

Humor me and tell me what you did ...

 

[chetzread]

Humor me and tell me what you did ...

？

 

[BvU]

You said

ok, i got the ans now

could you share your working with us ?