posted by Tiffany .
Find the volume using the shell method - about the x-axis
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.
It is y^(2/3) - we have not gone over shell method yet so.....
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
The limits are 0,3