Answer
$\frac{\pi}{6}$ $($$17$$\sqrt 17$ $-$ $5$$\sqrt 5$$)$
Work Step by Step
$x$ $=$ $y^{2}$ $-$$1$
$\frac{dx}{dy}$ $=$ $2y$
$2$$\pi$$\int_{0}^{3}$ $\sqrt {x+1}$
$=$$\int_{0}^{3}$ $2 \pi$ $\sqrt {x+\frac{5}{4}}$$dx$
$=$$\frac{4}{3}$ $\times$ $\frac{1}{8}$$\pi$$($$17$$\sqrt 17$ $-$ $5$$\sqrt 5$$)$
$=$ $\frac{\pi}{6}$ $($$17$$\sqrt 17$ $-$ $5$$\sqrt 5$$)$
