Question

Calcular la función primitiva determinando el valor de la constante de integración de:
-S'=2t^2-10t+1, sabiendo que S(0)=3

Answer 1

-S' = 2t²-10t+1

S' = -2t²+10t-1

$\frac{dS}{dt} = -2 t^{2} +10t -1$

dS = (-2t²+10t-1)dt

∫ dS = ∫ (-2t²+10t-1)dt

S = -2 ∫ t² dt + 10 ∫ t dt - ∫ dt

$S = \frac{-2}{3} t^{3} + 5 t^{2} - t + C$

Si S(0) = 3 entonces

t = 0 y S = 3

3 = 0 + 0 + 0 + C

→ C = 3

∴ $S = - \frac{2}{3} t^{3} + 5 t^{2} - t + 3$