Volume of Solids of Revolution

[olicoh]

Homework Statement

In Problems 1-5, let R be the region bounded by y√x =, y = 1, and x = 4. Each problem will describe a solid generated by rotating R about an axis. Write an integral expression that can be used to find the volume of the solid (do not evaluate).
I only need help with problem 2: The solid is generated by rotating R about the y-axis.

The Attempt at a Solution

I got V=pi∫[1,3](y^4-16)dy
My teacher says I got my bounds wrong? I'm not sure why she thinks that. I though [1,3] on the y-axis were the bounds for this equation.

 

[mighty2000]

I understand that you are trying to find the volume of a solid generated by rotating the region R about the y-axis. Your integral expression, V=pi∫[1,3](y^4-16)dy, is close, but your bounds are incorrect. In this case, the bounds should be [0,1] since the region R is bounded by y=1 on the upper boundary and y=√x on the lower boundary. Therefore, the correct integral expression would be V=pi∫[0,1](y^4-√x)dy. I hope this helps clarify the issue. Good luck with your problem solving!