Answer
$\dfrac{28 \pi}{3}$
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2}$
Now, $S =(2 \pi)\int_{(3/4)}^{(15/4)} \dfrac{1}{2} [\sqrt {4x+1}] dx \\= \dfrac{\pi}{6} [(4x+1)^{3/2}]_{3/4}^{15/4} \\=\dfrac{28 \pi}{3}$
