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Could you check my solution? $$\iint_D \frac{y}{\sqrt{x^2 + y^2}} \, dx\,dy, D = \Big\{(x, y) ~\Big|~ \frac 3 2 ay \le x^2 \le a^2 - y^2 \Big\} = \\ 2\left( \int_{-\frac{\pi}{2}}^0 d \varphi \int_0^a \sin\varphi \, dr + \int_0^{\frac \pi 6} d \varphi \int_{\frac{3a\sin\varphi}{2\cos^2 \varphi}}^a \sin\varphi \,dr \right) = \cdots$$

Thanks

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