How is τmax/rmax related to the second moment of area?

[Riazy]

Homework Statement

dT= τmax/rmax * r^2 dA

T = τmax/rmax ∫▒〖r^2 dA〗

as far as I am concerned integrating this will give us r^3/3 + c?
or am i thinking wrong, how did my teacher get the answer below in bold

Homework Equations

its not a great deal to do but I don't know how my professor got the following answer below

The Attempt at a Solution

the question is why the answer to this is

τ/rmax * Ip

 

[rock.freak667]

The second moment of area is defined as

$$I = \int_A r^2 dA$$


had you ∫r² dr, then you'd get r³/3 + C