Integral Calculus Including Differential — Equations

[ \frac{dv}{dr} + \frac{v}{r} = 3r^2 ]

[ r \frac{dv}{dr} + v = 3r^3 ]

"48 flux-units," she whispered.

Now came the integral calculus. The total destructive potential ( P ) was the integral of velocity across the whirlpool’s radius ( R ) (which was 4 meters): Integral calculus including differential equations

The integrating factor ( \mu(r) ) was:

[ v(r) = \frac{3}{4} r^3 ]

Integrating both sides with respect to ( r ): [ \frac{dv}{dr} + \frac{v}{r} = 3r^2 ] [