[tex]\displaystyle\iint_D(4x-6y)\,\mathrm dA=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=5}r(4r\cos\theta-6r\sin\theta)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]\displaystyle=\int_{\theta=0}^{\theta=2\pi}\left(\frac43\cos\theta-2\sin\theta\right)r^3\bigg|_{r=0}^{r=5}\,\mathrm d\theta[/tex]
[tex]\displaystyle=125\int_{\theta=0}^{\theta=2\pi}\left(\frac43\cos\theta-2\sin\theta\right)\,\mathrm d\theta[/tex]
[tex]\displaystyle=125\left(\frac43\sin\theta+2\cos\theta\right)\bigg_{\theta=0}^{\theta=2\pi}[/tex]
[tex]=125(250-250)=0[/tex]
