Find the volume of the solid formed by revolving the region bounded by y=x^2+1, y=0, x=0, and x=1 about the y-axis.
I was practicing this concept and I came across this problem. I did it using the shell method and got 2pi*Integral of x(x^2+1) from 0 to 1, which yielded the answer 3pi/2.
I tried checking this with the disc/washer method, but this gave me a different answer. Pi*Integral of [Sqrt(y-1)]^2 from 1 to 2 = pi/2.
Likewise, I tried a similar problem with the functions: y = Sqrt(x), x=axis, and x=4 roated about the x=8
Cylinders: 2piIntegral of Sqrt(x)(8-x) from 0 to 4 = 896pi/15 Disk/Washers: pi*Integral of (8-y^2)^2 from 0 to 2 = 1376pi/15
Which ones are correct? Where did I make mistakes?