MATH 1310.03F A **Quiz 2** Thursday, September, 28 2000

NAME:

Student Number: No.Marks

(25 Marks) Find the volume *V* of the solid of revolution obtained by
revolving the region bounded by the graphs of and
*g*(*x*)=*x*+1 around the x-axis.

Solution: 1. Find the intersection points of *f*(*x*) and *g*(*x*).

Let *f*(*x*)=*g*(*x*), i.e. . Then

This implies

2. Look for regions.

Since ,

for , i.e., for and

for , i.e., for .

Hence, we obtain two regions:

*y*=*f*(*x*), *y*=*g*(*x*) for ,
*a*=-1 and *b*=0.

*y*=*g*(*x*), *y*=*f*(*x*) for ),
*a*=0 and *b*=-1.

3. Find out the axis of revolution given in the question.

The axis of revolution: x-axis.

4. Apply the corresponding formula to and .

and

5. Compute the volume .

Thu Sep 28 10:19:02 EDT 2000