#### To determine

**To find:**

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

#### Answer

V=43π unit3

#### Explanation

**1) Concept:**

The volume of the washer obtained by the revolution about the x-axis is

V= ∫abπouter radius2-inner radius 2dx

**2) Given:**

The region bounded by y2-x2=1, y=2, rotated about the x- axis.

**3) Calculation:**

The graph of the region bounded by the given curves is

Find the volume of the solid by using the washer method.

Here, the region is bounded by y2-x2=1⇒y=±x2+1 and y=2

The outer radius is y=2 and the inner radius is x2+1. At intersection of both curves x2+1=2 That is x2+1=4. So x=3,-3 Thus

V=∫-33π2-02-1+x2-02dx

∫-33π4-1+x2dx

By the symmetry,

2∫03π3-x2dx

=2π3x-13x303

=2π[33-1333-0 ]

=2π 33-3

V=43 π

**Conclusion:**

The volume of the solid obtained by rotating the region bounded by the given curves is

V=43 π unit3