(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral

[tex]\int\limits_{V=\infty} e^{-r} \left[ \nabla \cdot \frac {\widehat{r}} {r^2} \right] , d^3 x[/tex]

2. Relevant equations

Divergence theorem:

[tex]\int\limits_{V} \left ( \nabla \cdot A \right ) \, d^3 x

= \oint\limits_{S} A \cdot \, da}

[/tex]

3. The attempt at a solution

I know that I have to apply the div theorem somewhere, but this [tex]e^{-r}[/tex] is confusing and what does it mean if the lower limit V is infinity?

I haven't seen the integral of [tex]\frac{1}{e^r} [/tex] before but I'm kinda guessing

[tex] \int \frac{1}{e^r} \, dr

= \frac{1}{e^r} \int \frac{1}{u} \frac{du}{e^r}

= ln(e^r)

= r

[/tex]

where I used a substitution [tex]u=e^r[/tex] and [tex]du= e^r dr[/tex]

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# Homework Help: Integral with divergence thm

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