Assuming you're computing the volume of the region [tex]E[/tex], we have upon converting to cylindrical coordinates,
[tex]\displaystyle\iiint_E\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/2}\int_{\theta=0}^{\theta=\pi/2}\int_{\rho=3}^{\rho=5}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\frac\pi2\left(\int_0^{\pi/2}\sin\varphi\,\mathrm d\varphi\right)\left(\int_3^5\rho^2\,\mathrm d\rho\right)[/tex]
[tex]=\dfrac{49\pi}3[/tex]
