Integral Calculus Including Differential Equations ⇒ [ TOP-RATED ]

Integrating both sides with respect to ( r ):

"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{d}{dr}(r v) = 3r^3 ]

Lyra paused. At the center ( r \to 0 ), velocity couldn’t be infinite (no whirlpool tears a hole in reality). So ( C = 0 ). The true function was clean and smooth: Integrating both sides with respect to ( r

[ P = \int_{0}^{R} v(r) , dr = \int_{0}^{4} \frac{3}{4} r^3 , dr ] Solve for ( v(r) ), then integrate it

"48 flux-units," she whispered.