integral from 0 to 1 of (10e^{2t}-7)

Lösung

\int_{0}^{1} (10 e^{2 t} - 7) d t

5 e^{2} - 12

Dezimale

24.94528 \dots

Schritte zur Lösung

\int_{0}^{1} 10 e^{2 t} - 7 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_{0}^{1} 10 e^{2 t} d t - \int_{0}^{1} 7 d t

\int_{0}^{1} 10 e^{2 t} d t = 5 (e^{2} - 1)

\int_{0}^{1} 7 d t = 7

= 5 (e^{2} - 1) - 7

Vereinfache

5 (e^{2} - 1) - 7 : 5 e^{2} - 12

= 5 e^{2} - 12

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