Urgent help with integral and LN expression

[OrangeOne]

Hi all,

I need help with the following task:

Calculate
?? ln(1+x^2+y^2) dxdy
D

where D is: (x,y); 1 <=x^2+y^2<=2

(<= means bigger than or equal to)

I think I should use polar coordinates where

x= r cos §
y= r sin §

Then I get:

?? ln(1+r^2)

? dr goes from 1 to 2
? d§ goes from 0 to 2 pi

But what is the integral of ln(1+r^2)?


I really need help,

thanks!

 

[Deleted member 4993]

Hi all,

I need help with the following task:

Calculate
?? ln(1+x^2+y^2) dxdy
D

where D is: (x,y); 1 <=x^2+y^2<=2

(<= means bigger than or equal to)

I think I should use polar coordinates where

x= r cos §
y= r sin §

Then I get:

?? ln(1+r^2)

? dr goes from 1 to 2
? d§ goes from 0 to 2 pi

But what is the integral of ln(1+r^2)?


I really need help,

thanks!

You know that you have to change "dx.dy" to "r.dr.d?"

Does that help??

 

[galactus]

You are correct, except for the missing r SK mentioned.

Your polar integral will be

\(\displaystyle \int_{0}^{2\pi}\int_{1}^{2}rln(1+r^{2})drd{\theta}\)

You can start off by letting \(\displaystyle u=1+r^{2}, \;\ \frac{du}{2}=rdr\)

Always remember to add the extra 'r' when using polar double integration.