Integral: Calculus Including Differential Equations

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

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

"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

[ 4^4 = 256, \quad \frac{3}{16} \times 256 = 3 \times 16 = 48 ] [ v(r) = \frac{3}{4} r^3 ] [ \frac{d}{dr}(r

[ P = \int_{0}^{R} v(r) , dr = \int_{0}^{4} \frac{3}{4} r^3 , dr ] " said her master