i_{k i n n i n e} = \int J d A = \int_{a}^{r} c r^{2} (2 π r d r) = 2 π c \int_{a}^{r} r^{3} d r = 2 π c {[\frac{r^{4}}{4}]}_{a}^{r} = \frac{π c (r^{4} - a^{4})}{2}

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

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