- #1
asmani
- 105
- 0
Hi all.
Suppose that we want to compute the following indefinite integral:
The correct solution by Mathematica:
Now here is the (apparently) incorrect solution by using polar coordinates:
[tex]\iint\frac{1}{\sqrt{x^2+y^2}}dxdy=\iint\frac{1}{r}rdrd\theta=(r+c_1)(\theta+c_2)[/tex]
If c1=c2=0, then one solution is:
[tex]r\theta=\sqrt{x^2+y^2}\tan^{-1}\left ( \frac{y}{x} \right )[/tex]
But it isn't:
What's wrong with this solution?
Thanks in advance.
Suppose that we want to compute the following indefinite integral:
The correct solution by Mathematica:
Now here is the (apparently) incorrect solution by using polar coordinates:
[tex]\iint\frac{1}{\sqrt{x^2+y^2}}dxdy=\iint\frac{1}{r}rdrd\theta=(r+c_1)(\theta+c_2)[/tex]
If c1=c2=0, then one solution is:
[tex]r\theta=\sqrt{x^2+y^2}\tan^{-1}\left ( \frac{y}{x} \right )[/tex]
But it isn't:
What's wrong with this solution?
Thanks in advance.