Determine whether the statement is true or false, and explain why.
the volume of the solid formed by revolving the function f(x) = √x^2+1 about the x-axis on the interval [1, 2] is given by ∫^2_1π√x^2+1 dx.

The statement is true

Step-by-step explanation:

Volume of a Solid of revolution:

when a region in the plane is revolved about a given line that is called axis of revolution, then we get a solid of revolution.

In this problem we want to find the volume of a solid formed by revolving the function about the x-axis on the interval [1,2]

We can find the volume of any solid by integrating its area

    eq. 1

where

and

Limits are

eq. 1 becomes

Hence proved.

The volume of the solid formed by revolving the function  about the x-axis on the interval [1, 2] is given by

7

step-by-step explanation: