Answer
$\dfrac{49 \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_{2}^{6} \sqrt {y} \sqrt {\dfrac{4y+1}{4y}}dy$
or, $=\dfrac{\pi}{4} [\dfrac{2(4y+1)^{3/2}}{3}]_2^6$
or, $= \dfrac{49 \pi}{3} $
