f^'(x)=x^2-x,f(3)= 19/2

解

f^{^{'}} (x) = x^{2} - x, f (3) = \frac{19}{2}

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 5

解答ステップ

f^{'} (x) = x^{2} - x

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

であれば

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

f (x) = \int x^{2} - x d x

\int x^{2} - x d x = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + c_{1}

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + c_{1}

初期条件を適用する:

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 5

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 5