I keep finding a negative volume for this solid of revolution. Please help?
Find the volume of the solid of revolution formed by revolving the planar region, and , about the y-axis. You may choose either the shell or the disk method.
Here is what I did:
v = pi*[integral from 0 to 1 of (y^2 - (cube root(y))^2)dy]
= pi*[integral from 0 to 1 of (y^2 - y^(2/3))dy]
= pi*(1/3y^3 - 3/5y^5/3)
= pi*(1/3 - 3/5)
= pi*(5/15 - 9/15)
I'm pretty sure I can't have a negative volume, can I? What did I do wrong?
Also, how do you use the math tags to write a definite integral?