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

Lösung

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

\frac{11}{6}

Dezimale

1.83333 \dots

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{7}{3} - \frac{1}{2} : \frac{11}{6}

= \frac{11}{6}

\int_{3}^{5} 7 d x

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