Hi I'm trying to integrate the following [itex]q_m = -D A \frac{dc}{dx}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

where [itex]A = 4 \pi r^2[/itex] Yes, a sphere.

My supplied literature simplifies to [itex]q_m = -D 2 \pi r L \frac{dc}{dr}[/itex] when [itex]A = 2 \pi r L [/itex]

Integrating to [itex]\int_{r1}^{r2} q_m \frac{dr}{r} = - \int_{c1}^{c2} 2 \pi L D dc[/itex]

Integrated to [itex]q_m ln \frac{r_2}{r_1} = 2 \pi L D (c_1 - c_2) [/itex]

I've had a go but unsure what to do with the [itex]r^2[/itex]

I thought this might work but it gives a negative value for [itex]q_m[/itex]

[itex]\int_{r1}^{r2} q_m \frac{dr}{r^2} = - \int_{c1}^{c2} 4 \pi D dc[/itex]

Integrated to [itex]q_m ln \frac{r_2}{r_1^2} = 4 \pi D (c_1 - c_2) [/itex]

Any ideas? Thanks.

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# Integration - slightly confused

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