\(\displaystyle

\int_{}^{} \int_{}^{} \int_{}^{} y dxdydz

\)

I managed to setup the following boundary, but it yielded zero

\(\displaystyle

\int_{-1}^{2} \int_{-sqrt(3)}^{sqrt(3)} \int_{-sqrt(3-y^2)}^{sqrt(3-y^2)} y dxdydz

\)

so.. I reshape the boundaries to avoid getting zero...

\(\displaystyle

\int_{-1}^{2} \int_{0}^{sqrt(3)} \int_{0}^{sqrt(3-y^2)} 4 * y dxdydz

\)

This new boundaries yields 12 * sqrt(3).

But to my surprise the correct answer is 6 * sqrt(3).

Any idea where I got wrong??