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

Lösung

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

\frac{5}{6}

Dezimale

0.83333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

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

= \frac{7}{3} - 2 + \frac{1}{2}

Vereinfache

\frac{7}{3} - 2 + \frac{1}{2} : \frac{5}{6}

= \frac{5}{6}

(1 - x^{2}) y^{^{'}} - x^{2} y = (1 + x) 1 - x^{2}

\int (x^{3} + x) d x

\frac{d}{d x} (arcsin (2 x))

\frac{\partial}{\partial x} (y ln (x))

\int 12 t^{3} d t