Answer
$\dfrac{28 \pi}{3}$
Work Step by Step
Integrate the integral to calculate the surface area as follows:
We have: $S_{A}= (2 \pi)\int_{a}^{b} y \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =(2 \pi)\int_{3/4}^{15/4} \dfrac{\sqrt {4x+1}}{2} dx$
or, $= \dfrac{\pi}{6} [(4x+1)^{3/2}]_{3/4}^{15/4}$
Thus, $Surface \space Area=\dfrac{28 \pi}{3}$
