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


Nepsesh

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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 by Nepsesh
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