Answer
The statement is False.
Work Step by Step
The statement is False.
The volume of the solid formed by revolving the function $f(x) $
about the x-axis on the interval [a, b] is given by
$$
\int_{a}^{b} \pi [f(x)]^{2}dx
$$
So,the volume of the solid formed by revolving the function $f(x)=\sqrt {x^{2}+1} $ about the x-axis on the interval [1, 2] is given by
$$
\begin{aligned}
\int_{1}^{2} \pi [\sqrt {x^{2}+1}]^{2}dx&=\int_{1}^{2} \pi (x^{2}+1)dx\\
&\ne \int_{1}^{2} \pi (\sqrt {x^{2}+1})dx
\end{aligned}
$$
Therefore, the statement is False.