integral from 3 to 6 of 10^8((t^2)/3+1)

Lösung

\int_{3}^{6} 1 0^{8} (\frac{t ^{2}}{3} + 1) d t

2400000000

Schritte zur Lösung

\int_{3}^{6} 1 0^{8} (\frac{t ^{2}}{3} + 1) d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 1 0^{8} \cdot \int_{3}^{6} \frac{t ^{2}}{3} + 1 d t

Vereinfache

= 100000000 \cdot \int_{3}^{6} \frac{t ^{2}}{3} + 1 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

= 100000000 (\int_{3}^{6} \frac{t ^{2}}{3} d t + \int_{3}^{6} 1 d t)

\int_{3}^{6} \frac{t ^{2}}{3} d t = 21

\int_{3}^{6} 1 d t = 3

= 100000000 (21 + 3)

Vereinfache

= 2400000000

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