Calculate the following double integral using polar coordinates: $\iint_{D}^{}\frac{dxdy}{1+x^{2}+y^{2}}$
$D = \left \{(x,y) | 0\leq y\leq \sqrt{1-x^{2}} \right \}$
I have started solving but pretty sure I have mistakes.
The region is:
And I know that:
$x=r\cdot cos(\theta )$
and
$y=r\cdot sin(\theta )$
also
$x^{2}+y^{2}=r^{2}$
From the region it is clear that
$0\leq r\leq 1$
and
$0\leq \theta \leq \pi $
so I thought (and probably wrong):
$\iint_{}^{}\frac{1}{1+r^{2}}drd\theta =\theta \cdot arctan(\theta )$