next up previous
Next: About this document

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

NAME:

Student Number:tex2html_wrap_inline196 No.tex2html_wrap_inline198Marks tex2html_wrap_inline200


(25 Marks) Find the volume V of the solid of revolution obtained by revolving the region bounded by the graphs of tex2html_wrap_inline204 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. tex2html_wrap_inline216. Then
displaymath218

This implies
displaymath220

2. Look for regions.

Since tex2html_wrap_inline224,

tex2html_wrap_inline226 for tex2html_wrap_inline228, i.e., tex2html_wrap_inline230 for tex2html_wrap_inline228 and

tex2html_wrap_inline234 for tex2html_wrap_inline236, i.e., tex2html_wrap_inline238 for tex2html_wrap_inline236.

Hence, we obtain two regions:

tex2html_wrap_inline242 y=f(x), y=g(x)tex2html_wrap_inline248 for tex2html_wrap_inline250, a=-1 and b=0.

tex2html_wrap_inline256 y=g(x), y=f(x) tex2html_wrap_inline262 for tex2html_wrap_inline236), 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 tex2html_wrap_inline274 and tex2html_wrap_inline276.


eqnarray39

and


eqnarray107

5. Compute the volume tex2html_wrap_inline280.


eqnarray161




Kunquan Lan
Thu Sep 28 10:19:02 EDT 2000