Math Help - Cylindrical shell question

1. Cylindrical shell question

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis.

My graph is the parabola y=5x^2 up to the line x=1 and rotated around y axis and makes a bowl-like shape

Formula for cylindrical shell:

integral from a to b (2pi(r)(height)dy

So I did integral from 0 to 1
dy

Am I correct or am I doing something wrong?

2. Re: Cylindrical shell question

The region is you have specified is not bounded. Are you sure you copied it down right?

3. Re: Cylindrical shell question

Sorry, I am not sure. I though the bounds are 0 and 1 since y=0 and x=1 but I guess that is incorrect.

I solved y=5x^2 for x and got x= sqrt(y/5) but I am not sure where to go from there.

formula for cylindrical is: integral a to b 2pi(radius)heightdy

I am thinking the height is sqrt(y/5)? or do I have to subtract from the line x=1? Im a little perplexed with this problem.

4. Re: Cylindrical shell question

Try drawing the region with your bounds, you'll see it is definitely not bounded. Perhaps you meant y = 1 instead of x = 1...

5. Re: Cylindrical shell question

I figured this out:
y=5x^2 , y=0 , x=1

5x^2 being the height and x being the radius

integral 0 to 1 2pi(x)*5x^2 dx

10pi integral 0 to 1 x^3

5pi/2 final ans.