integral from 1 to 2 of (2x^2)-(2x+6)

Lösung

\int_{1}^{2} (2 x^{2}) - (2 x + 6) d x

- \frac{13}{3}

Dezimale

- 4.33333 \dots

Schritte zur Lösung

\int_{1}^{2} 2 x^{2} - (2 x + 6) d x

Vereinfache

= \int_{1}^{2} 2 x^{2} - 2 x - 6 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} 2 x^{2} d x - \int_{1}^{2} 2 x d x - \int_{1}^{2} 6 d x

\int_{1}^{2} 2 x^{2} d x = \frac{14}{3}

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

\int_{1}^{2} 6 d x = 6

= \frac{14}{3} - 3 - 6

Vereinfache

\frac{14}{3} - 3 - 6 : - \frac{13}{3}

= - \frac{13}{3}

t an g e n t \frac{x ^{2} - 1}{x ^{2} + x + 1} (1)

\int_{- \frac{π}{4}}^{\frac{π}{4}} x^{2} d x

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s im pl i f y \frac{x}{lo g _{e} ( x )}