integral of (x-7)^2

Lösung

\int (x - 7)^{2} d x

\frac{x ^{3}}{3} - 7 x^{2} + 49 x + C

Schritte zur Lösung

\int (x - 7)^{2} d x

Multipliziere aus

(x - 7)^{2} : x^{2} - 14 x + 49

= \int x^{2} - 14 x + 49 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 x^{2} d x - \int 14 x d x + \int 49 d x

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

\int 14 x d x = 7 x^{2}

\int 49 d x = 49 x

= \frac{x ^{3}}{3} - 7 x^{2} + 49 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 7 x^{2} + 49 x + C

n = 1 \sum \infty \frac{1}{2 ^{n - 1}}

x \to \infty lim (0^{0})

x \to 3 lim (\frac{1}{( x - 3 )})

\int_{0}^{1} 2 x^{2} (x^{3} - 1)^{3} d x

\int x^{2} - 16 d x