- #1

Liondancer

- 8

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## Homework Statement

I'm having a bit of trouble when it comes to volume of revolutions and areas. I find it quite difficult when it comes to setting up the integral. I'm not sure when to use the shell or washer method. Could someone explain to me or give me a tutorial on how to set up the equations thanks!

Here are a few examples

1)Find the volume of the solid obtained by rotating the region enclosed by the curves y=x^2 , x = 3, x = 8, and y=0 about the line x=9.

2)The region enclosed by the curves y = x^2 and x = y^2 is rotated about the line y = -2. Find the volume of the resulting solid.

3)Find the volume of the solid formed by rotating the region enclosed by the curves y=e^(x) + 2, y=0 , x=0, and x=0.1 about the x-axis.

4)Find the volume of the solid obtained by rotating the region enclosed by the curves y=x^2 and x = y^2 about the line x=-1.

5)The region enclosed by the curves x = 1 - y^4 and x = 0 is rotated about the line x = 4. Find the volume of the resulting solid.

Thanks for all the help!

## Homework Equations

regular integration equations?

## The Attempt at a Solution

1) (integral 9 top 3 bottom) pi(81-x^4)dx

2) (integral 1 top 0 bottom) 2pi(x^2 - x^.5)(2+x)dx

3) (integral 1 top 0 bottom) pi((e^(x) + 2)^2)dx

4) (integral 1 top 0 bottom) 2pi(x^2 - x^.5)(1+x)dx

5) not sure

thanks for all the help!