Integral Calculus Including Differential Equations < LEGIT >

Thus, the velocity profile was:

[ 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):

"Here," said her master, old Kael, handing her a data slate. "This equation models how the spin changes with radius. The whirlpool’s total destructive potential is the area under the velocity curve from ( r=0 ) to ( r=R ). Solve for ( v(r) ), then integrate it. That area is the energy you must dissipate." Integral calculus including differential equations

[ \frac{dv}{dr} + \frac{1}{r} v = 3r^2 ]

She multiplied through:

[ \mu(r) = e^{\int \frac{1}{r} dr} = e^{\ln r} = r ]