integral from 1 to 4 of 3x^2-4+4/(x^2)

Lösung

\int_{1}^{4} 3 x^{2} - 4 + \frac{4}{x ^{2}} d x

54

Schritte zur Lösung

\int_{1}^{4} 3 x^{2} - 4 + \frac{4}{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}^{4} 3 x^{2} d x - \int_{1}^{4} 4 d x + \int_{1}^{4} \frac{4}{x ^{2}} d x

\int_{1}^{4} 3 x^{2} d x = 63

\int_{1}^{4} 4 d x = 12

\int_{1}^{4} \frac{4}{x ^{2}} d x = 3

= 63 - 12 + 3

Vereinfache

= 54

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