Could you help me with the following please: Evaluate
$$\iint_{U} \frac{x}{y+x^{2}}dxdy$$
where $U$ is limited by $x = 1$, $y=x^{2}$, $y=4-x^{2}$. Suggestion consider $x=\sqrt{v-u}$ and find $y$ as a function of $u$ and $v$ and apply change of variable.
I have plotted the region and searched how to find $y$, to obtain the transformation and to be able to calculate the Jacobian, if you could please help me find it $y$ or if you could give me some advice, thank you.
$$\int_{1}^{\sqrt 2}dx \int_{x^2}^{4-x^2}\frac{x}{y+x^{2}}dy$$ imho is more easy direct integrating.