integral from 0 to 2 of (x-7)^2

Lösung

\int_{0}^{2} (x - 7)^{2} d x

\frac{218}{3}

Dezimale

72.66666 \dots

Schritte zur Lösung

\int_{0}^{2} (x - 7)^{2} d x

Multipliziere aus

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

= \int_{0}^{2} 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_{0}^{2} x^{2} d x - \int_{0}^{2} 14 x d x + \int_{0}^{2} 49 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 14 x d x = 28

\int_{0}^{2} 49 d x = 98

= \frac{8}{3} - 28 + 98

Vereinfache

\frac{8}{3} - 28 + 98 : \frac{218}{3}

= \frac{218}{3}

\int 3 a x d x

x \to 3 - lim (\frac{1}{x ^{2} - 9})

x \to 2 lim (\frac{4 - x ^{2}}{x})

t an g e n t y = x + x, (16, 20)

\frac{d y}{d x} + e^{x} y = 1