Assignment:
Find the volume of the solid generated when the region R bounded by the geven curves is revolved about the indicated axis. Do this by performing the following steps
- Sketch the region R
- Show a typical slice properly labeled
- Write a formula for the approximate volume of the shell generated by this slice
- Set up the corresponding integral
- Evaluate this integral
1. y= x^2 , x=I y=0 about the y axis
2. y=9 – x^2 ( x> 0 ), x=0 y=0
3. y=9-x^2 (x>0), x=0, y=o ; about the line x=3
4. y==x^2, y=3x ; about the y-axis
5. x = sqrt y + 1 y=4 , y=0 ; about the x-axis
6. x = sqrt 2y 1 , y= 2 x= 0 ; about the line y =3
Provide complete and step by step solution for the question and show calculations and use formulas.