integral from 0 to 1 of (x-1)^2

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

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

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

= \frac{1}{3} - 1 + 1

Vereinfache

= \frac{1}{3}

\int_{0}^{1} \frac{1}{1 + x ^{4}} d x

\int_{0}^{t} sin (t) d t

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\int_{e^{10}}^{\infty} \frac{2}{x} d x

\int_{- 2}^{0} 2 d x