I have a region bounded by the lines $y=x$, $y=2x$, and $y=1-x$
I need to evaluate
$$\iint_R\sin\left(\frac{3x}{2x+y}\right) dxdy$$
I already figured the bounds of the region require splitting the integral into two parts, however I'm having trouble with the actual integration:
$$\int_0^{\frac{1}{2}}{\int_y^\frac{y}{2}{\sin\left(\frac{3x}{2x+y}\right) dx}dy} + \int_{\frac{1}{2}}^\frac{2}{3}\int_\frac{y}{2}^{1-y} \sin\left(\frac{3x}{2x+y}\right)dxdy $$