Linear mss density (mass/length) of a rod depends on the distanec from one end (say A) as `lamda_(x)=(alphax+beta)` here `alpha` and `beta` are constants, find the moment of inertia of this rod about an axis passing through `A` and perpendicular to the rod. Length of the rod is `l`.

Explanation

`I=int_(0)^(I)dI=int_(0)^(l)(dm)x^(2)`
`=int_(0)^(l)(lamda_(X)dx)x^(2)`
`=int_(0)^(l)(alphax+beta)x^(2)dx`
`=(alphal^(4))/(4)+(betal^(3))/(3)`