Posted by **Tiffany** on Friday, April 12, 2013 at 10:39am.

Find the volume using the shell method - about the x-axis

x=y^2/3

- Calculus -
**Steve**, Friday, April 12, 2013 at 11:13am
v = ∫2πrh dy

where r=y and h=x

v = 2π∫xy dy

Can't tell whether you mean (y^2)/3 or y^(2/3)

anyway, plug it in and use the appropriate limits.

- Calculus -
**Tiffany**, Friday, April 12, 2013 at 3:23pm
It is y^(2/3) - we have not gone over shell method yet so.....

- Calculus -
**Steve**, Friday, April 12, 2013 at 4:00pm
so, you have

v = 2π∫(y^(2/3))y dy

= 2π∫y^(5/3) dy

= 2π (3/7) y^(7/3)

but you need to specify the limits of integration, since the curve is open-ended.

visit wolframalpha.com and enter

plot y^2 = x^3

- Calculus -
**Tiffany**, Saturday, April 13, 2013 at 6:25pm
The limits are 0,3

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