26-5-7

Find moment of inertia with respect to x axis.

x = -1, x = 1, y = 0, y = 1

Attempt:

Ix = 2pi(k) (int) (1)y^3 dy

boundaries 1 and 0

= 2pi(k)1/4(y^4)

= (2pi(k))/4 = Ix

m = 2pi(k) (int) xy dy

= 2pi(k) (int) (1)y dy

= 2pi(k)1/2(y^2)

= pi(k)(y^2) = pi(k)

R^2 (subscript x) = [(2pi(k))/4]/[(pi(k)]

K = 1 (from appearances of book example questions)

R^2 (subscript x) = 0.5

R (subscript x) = sqrt(0.5)

the book answer is 2/3k though. What did I do wrong? thanks