Some error in integrals of x-axis rotation of solids for Y=x^2

[Nepsesh]

Please help. My attempt to rotate the volume about the x-axis of y=x^2, first by disk method, then by shell method produces two answers - where obviously it should be the same answer. The limits are from 1 to 0.

 

1. V=Pi int(x^2)^2 dx = Pi int(y^4)dx = Pi/5 = 0.62631 ft cbd. (Disk method using f(x) where y=x^2).

 

2. V=2Pi int y.(sqrt y) dy = 4xPi/5 = 2.51327 ft cbd. (Shell method using g(y) where x=sq rt y).

 

 

Couldn't be simpler? I've spent hours trying to see what's wrong.

Edited March 4, 2016 by Nepsesh

[mathematic]

disc method: [latex]\pi \int_0^1 2x(1-x^2)dx[/latex]

shell method: [latex]\pi \int_0^1 ydy[/latex]

both methods give volume = [latex]\frac{\pi}{2}[/latex]

Edited March 5, 2016 by mathematic

[Nepsesh]

Thanks so much for your answer, my error was in the (1-x^2) shell's 'height' assembly, ie missing the 1- from the limit. Much obliged, M.