- #1

x^2

- 21

- 1

**Integration to Form a Solid -- Using Shells?**

## Homework Statement

Use the shell method to find the volumes of solids generated by revolving the shaded regions

about the indicated axes. The graph shows the equations:

[tex]x = \dfrac{y^4}{4}-\dfrac{y^2}{2}[/tex]

and

[tex]x = \dfrac{y^2}{2}[/tex]

a) The x-axis

b) The line y = 2

c) The line y = 5

d) The line y = -5/8

## Homework Equations

Shell method: [tex]V = 2\pi\int_a^b \! y * f(y) \, dy [/tex]

## The Attempt at a Solution

I attempted to use the shell method to find the volume of the formed "bowl" but I get a negative number:

[tex]V = 2\pi\int_0^2 \! y * (\dfrac{y^4}{4}-\dfrac{y^2}{2} - \dfrac{y^2}{2}) \, dy = 2\pi\int_a^b \! y * (\dfrac{y^4}{4}-y^2) \, dy = 2\pi\int_a^b \! (\dfrac{y^5}{4}-y^3) \, dy = 2\pi[\dfrac{y^6}{24} - \dfrac{y^4}{4}]^2_0 = 2\pi[\dfrac{64}{24} - \dfrac{16}{4}][/tex]

Where am I going wrong?

Thanks,

- x^2