integral from 1 to 3 of (t^6-t^2)/(t^4)

Lösung

\int_{1}^{3} \frac{t ^{6} - t ^{2}}{t ^{4}} d t

8

Schritte zur Lösung

\int_{1}^{3} \frac{t ^{6} - t ^{2}}{t ^{4}} d t

Multipliziere aus

\frac{t ^{6} - t ^{2}}{t ^{4}} : t^{2} - \frac{1}{t ^{2}}

= \int_{1}^{3} t^{2} - \frac{1}{t ^{2}} d t

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}^{3} t^{2} d t - \int_{1}^{3} \frac{1}{t ^{2}} d t

\int_{1}^{3} t^{2} d t = \frac{26}{3}

\int_{1}^{3} \frac{1}{t ^{2}} d t = \frac{2}{3}

= \frac{26}{3} - \frac{2}{3}

Vereinfache

\frac{26}{3} - \frac{2}{3} : 8

= 8

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