Consider the given curves to do the following.
x=4sqrt(y)
x = 0
y = 1
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Question

Consider the given curves to do the following. 
x=4sqrt(y)
x = 0
y = 1
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.

anonymous · Answer

Draw a diagram to visualize the problem.

anonymous · Answer

i put it so that its in x terms. so its y = (x^2)/16. am i able to do that?

anonymous · Answer

Yes you can

anonymous · Answer

$$2\pi \int\limits_{0}^{1}y(4y^(1/2))dy$$

anonymous · Answer

sorry its suppose to be 4y^1/2

anonymous · Answer

is that set up correctly?

anonymous · Answer

Let me calculate.

anonymous · Answer

Sorry, had to take a call. This has a little space between the function and x axis.

anonymous · Answer

its okay. and yeah it does

anonymous · Answer

How did you determine the boundary of 1?

anonymous · Answer

o, oops
i think i got it confused for the y=0

anonymous · Answer

how do you determine the boundary for this integral?

anonymous · Answer

o wait sorry

anonymous · Answer

If given freedom you would use washer technique. Instructions call for cylindrical shells, I think, check on this$$\int\limits_{0}^{4}2\pi(1-4\sqrt{y})4\sqrt{y}$$