f^'(s)=10s-12s^3,f(3)=2

解

f^{^{'}} (s) = 10 s - 12 s^{3}, f (3) = 2

f (s) = 5 s^{2} - 3 s^{4} + 200

解答ステップ

f^{'} (s) = 10 s - 12 s^{3}

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

f (s) = \int 10 s - 12 s^{3} d s

\int 10 s - 12 s^{3} d s = 5 s^{2} - 3 s^{4} + c_{1}

f (s) = 5 s^{2} - 3 s^{4} + c_{1}

初期条件を適用する:

f (s) = 5 s^{2} - 3 s^{4} + 200

f (s) = 5 s^{2} - 3 s^{4} + 200