(adsbygoogle = window.adsbygoogle || []).push({}); Integration to Form a Solid -- Using Shells?

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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

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# Homework Help: Integration to Form a Solid - Using Shells?

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