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Question

# The region between the curve $y=1 /(2 \sqrt{x})$ and the $x$-axis from $x=1 / 4$ to $x=4$ is revolved about the $x$-axis to generate a solid. Find the volume of the solid.

Solution

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In order to determine the volume of the rotating region, we will use the $\textcolor{#4257B2}{\textbf{disk method}}$, so first, we should determine the boundaries of the region, and then, using the mentioned method, get a specific integral that represents the value of the required volume.

The rotating region is bounded by the coordinate axes, the curve $y=\dfrac{1}{2\sqrt{x}}$, and the lines $x=\dfrac{1}{4}$ and $x=4$ and is located in the first quadrant.

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