$${i_{kinnine} = \int J\, dA = \int_a^r cr^2 (2 \pi r\, dr) \\ = 2 \pi c \int_a^r r^3\, dr = 2 \pi c \left[ \frac{r^4}{4} \right]_a^r \\ = \frac{\pi c (r^4 - a^4)}{2}}$$