例1
Find the area of the surface generated by revolving the curve 6xy=x+3 from |
|x=1 to x=3 about the x-axis.
【100 成大】
x++3x²
解:6.xy = x + 3 > y=
dv
1
1+(2)2 =₁/1+
1+-x
dx
4
所求表面積為
=
1
+
6x 6 2x
1
+
24x²
1
1
2
dy 1
--
dx 2
1
+---
2x²
x+
=
1
2x²
1
·x² +·
2
2x²