Chapter 5 - Applications of Integration - 5.2 Volumes - 5.2 Exercises - Page 374: 3

$8\pi $

$y=\sqrt{x-1}, y=0, x=5 ; \quad$ about the $x$-axis Here \begin{aligned} A(x)&= \pi f^2(x)\\ &= \pi (x-1) \end{aligned} find the intersection point \begin{aligned}\sqrt{x-1}&=0 \\ x&=1\end{aligned} Then the volume of the solid given by \begin{aligned} V&= \int_a^bA(x)dx\\ &= \pi\int_1^5(x-1)dx\\ &=\frac{\pi}{2} (x-1)^2\bigg|_1^5\\ &= 8\pi \end{aligned}