Question

The region bounded by the graph of f ( x ) = 1/1+x² and the x-axis between x = 0 and x = 2 is revolved about the x-axis. Find the volume of the solid that is generated. Round the answer to four decimal places.

Answer 1

The volume of the solid generated by revolving the region bounded by the graph of f(x) = 1/(1+x²) and the x-axis between x = 0 and x = 2 about the x-axis is approximately 4.9348.

Step-by-step explanation:

To find the volume of the solid generated by revolving the region bounded by the graph of f(x) = 1/(1+x²) and the x-axis between x = 0 and x = 2 about the x-axis, we can use the method of cylindrical shells.

The volume of the solid can be calculated using the formula: V = 2π ∫[a,b] x·f(x) dx.

In this case, a = 0 and b = 2. So, substituting the values into the formula, we have:

V = 2π ∫[0,2] x·(1/(1+x²)) dx

Simplifying and integrating, the volume is approximately 4.9348.