find the volume of the solid of revolution generated by revolving about the x - axis the region under the…

find the volume of the solid of revolution generated by revolving about the x - axis the region under the graph of $y = \\frac{2}{\\sqrt{x}}$ from $x = 2$ to $x = 5$.\nset up the integral that gives the volume of the solid.\n$\\int_{2}^{5} \\square dx$

find the volume of the solid of revolution generated by revolving about the x - axis the region under the graph of $y = \\frac{2}{\\sqrt{x}}$ from $x = 2$ to $x = 5$.\nset up the integral that gives the volume of the solid.\n$\\int_{2}^{5} \\square dx$

Answer

Explanation:

Step1: Recall volume - of - revolution formula

The formula for the volume $V$ of the solid of revolution about the $x$-axis using the disk method is $V=\pi\int_{a}^{b}[f(x)]^{2}dx$, where $y = f(x)$ is the function, and $[a,b]$ is the interval of integration.

Step2: Identify the function and interval

Here, $f(x)=\frac{2}{\sqrt{x}}$, $a = 2$, and $b = 5$.

Step3: Square the function

$[f(x)]^{2}=\left(\frac{2}{\sqrt{x}}\right)^{2}=\frac{4}{x}$.

Step4: Set up the integral

The integral for the volume is $\pi\int_{2}^{5}\frac{4}{x}dx$.

Answer:

$\pi\int_{2}^{5}\frac{4}{x}dx$