soisorce26
Member
- Joined
- Nov 30, 2006
- Messages
- 30
- Gender
- Male
- HSC
- 2007
can someone help me with the following questions:
1. The ellipse x²/a²+y²/b² = 1 is rotated about the line y=c (c>b). Find the volume formed by using the cylindrical shell method.
2. The region under the curve y=e^(-x²) and above the x-axis for -a<=x<=a is rotated about the y-axis to form a solid.
a)Divide the resulting solid into cylindrical shells S of radius t. Show that each shell S has approx. volume
dV = 2(pi) t e^(-t²)
where dt is the thickness of the shell.
b) What is the limiting value of the volume of the solid as a approaches infinity?
1. The ellipse x²/a²+y²/b² = 1 is rotated about the line y=c (c>b). Find the volume formed by using the cylindrical shell method.
2. The region under the curve y=e^(-x²) and above the x-axis for -a<=x<=a is rotated about the y-axis to form a solid.
a)Divide the resulting solid into cylindrical shells S of radius t. Show that each shell S has approx. volume
dV = 2(pi) t e^(-t²)
where dt is the thickness of the shell.
b) What is the limiting value of the volume of the solid as a approaches infinity?