integral from 0 to 8 of (x+1)^2

Lösung

\int_{0}^{8} (x + 1)^{2} d x

\frac{728}{3}

Dezimale

242.66666 \dots

Schritte zur Lösung

\int_{0}^{8} (x + 1)^{2} d x

Multipliziere aus

(x + 1)^{2} : x^{2} + 2 x + 1

= \int_{0}^{8} x^{2} + 2 x + 1 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}^{8} x^{2} d x + \int_{0}^{8} 2 x d x + \int_{0}^{8} 1 d x

\int_{0}^{8} x^{2} d x = \frac{512}{3}

\int_{0}^{8} 2 x d x = 64

\int_{0}^{8} 1 d x = 8

= \frac{512}{3} + 64 + 8

Vereinfache

\frac{512}{3} + 64 + 8 : \frac{728}{3}

= \frac{728}{3}

x \to 0 lim (\frac{ln ( 1 - 6 x )}{x})

x \to - 8 lim (\frac{∣ x + 8 ∣}{x + 8})

d er i v a t i v e - \frac{4 x}{y}

d er i v a t i v e f (x) = x cos (x)

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x