Volumes trouble.....cant see what ive done wrong (1 Viewer)

[RideTheLightnin]

hey guys, i dont understand what i have done wrong with this volumes questions
its exercise 6.1, 1d) in cambridge (yes its easy i know)

anyway
I rotate it around y=1, with the radii of my annulus being R=1 and r=y (where R>r)
so i get (let d = delta thing)
dV = pi(R^2-r^2)dx
= pi (1 - y^2)dx
= pi (1 - x^4)dx as y=x^2
so then i integrate that with my limit as dx approaching zero and having
a definite integral from 0 to 1.
I then get 4pi/5, when the answer gives me 7pi/15.
Where have i gone wrong?
Cheers

 

[Riviet]

Your inner radius r is incorrect because the inner radius is actually 1-y, not y. So your expression for the area of a slice should be pi[1-(1-y)²].

 

[RideTheLightnin]

ah yes it is too.....
thanks mate