integral of (100-x)^2

Lösung

\int (100 - x)^{2} d x

10000 x - 100 x^{2} + \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int (100 - x)^{2} d x

Multipliziere aus

(100 - x)^{2} : 10000 - 200 x + x^{2}

= \int 10000 - 200 x + x^{2} d x

Wende die Summenregel an:

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

= \int 10000 d x - \int 200 x d x + \int x^{2} d x

\int 10000 d x = 10000 x

\int 200 x d x = 100 x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 10000 x - 100 x^{2} + \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 10000 x - 100 x^{2} + \frac{x ^{3}}{3} + C

t an g e n t y = e^{- x^{2}}

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

\frac{\partial}{\partial y} (x e^{y} + y + 1)

\frac{d}{d t} (\frac{6 t + 28}{t + 7})

d er i v a t i v e f (x) = x^{3} (3 - x)^{4}