Answer
$\dfrac{28 \sqrt 2 \pi }{3}$
Work Step by Step
Integrate the integral to calculate the surface area as follows:
Surface area, $S=2\pi \int_{c}^{d}(y) \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =2 \pi \int_{0}^{3} \sqrt {2x+1} \sqrt {\dfrac{2x+2}{2x+1}} dx$
or, $=2 \sqrt 2 \pi \times (\dfrac{2}{3}) \times (8-1)$
or, $= \dfrac{28 \sqrt 2 \pi }{3}$
