MATH 1310.03F A Quiz 2 Thursday, September, 28 2000
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
2. Look for regions.
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 .
5. Compute the volume .