I have seen many videos and tutorials on how to sketch a region determined by double integrals however I am not sure on how to do this one because the example is slightly different from the videos I have seen. When I tried sketching this I got a semi-circle with the base on the y-axis, but I am not sure if it is correct. How do I sketch this one?
$$\int_{-1}^{1}\int_{0}^{\sqrt{1-y^2}}3dxdy$$
First, draw the lines $y=\pm1$ from the outer integral. Then the inner integral vary from $x=0$ to $x = \sqrt{1-y^2}$, which is a semicircunference with diameter in $y$-axis for $x\geq0$. This integral could be also written as $\int_{-1}^{1} 3\sqrt{1-y^2}dy$