integral from 1 to 4 of (1/2 x^2+x-1)

Lösung

\int_{1}^{4} (\frac{1}{2} x^{2} + x - 1) d x

15

Schritte zur Lösung

\int_{1}^{4} \frac{1}{2} x^{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_{1}^{4} \frac{1}{2} x^{2} d x + \int_{1}^{4} x d x - \int_{1}^{4} 1 d x

\int_{1}^{4} \frac{1}{2} x^{2} d x = \frac{21}{2}

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} 1 d x = 3

= \frac{21}{2} + \frac{15}{2} - 3

Vereinfache

\frac{21}{2} + \frac{15}{2} - 3 : 15

= 15

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