#### To determine

**To find:**

Approximate x coordinate of the points of intersection of the given curves by using the graph, and then use the calculator to find (approximately) the volume of the solid obtained by rotating the bounded region about x axis.

#### Answer

a) x coordinate of the points of intersection: x=0 and x 1.755

b) V≈3.145

#### Explanation

**1) Concept:**

i. If the cross section is a washer with inner radius rin and outer radius rout, then area of the washer is obtained by subtracting the area of the inner disk from the area of the outer disk,

A=π outer radius2 -π inner radius2

ii. The volume of the solid of revolution about the x-axis is

V= ∫abA(x)dx

**2) Given:**

y=2x-x23, y=x2x2+1; about the x axis

**3) Calculation:**

Region bounded by given curves is shown below:

From the above graph,

x coordinate of the points of intersection: x=0 and x 1.755

The cross section is perpendicular to the x-axis, and it is a washer.

Thus, the outer radius is the distance from the curve y= 2x-x23 to the axis of rotation x-axis, and the inner radius is the distance from the curve x2x2 + 1 to the axis of rotation x-axis.

So the outer radius is 2x-x23 and inner radius is x2x2 + 1

By using the concept

V =π∫01.7552x-x232-x2x2+12dx

V ≈3.145 ………………..by using calculator

Therefore,

x coordinate of the points of intersection: x=0 and x 1.755

V≈3.145

**Conclusion:**

x coordinate of the points of intersection: x=0 and x 1.755

V≈3.145