integral from 0 to t of 12e^{2x}-12e^x

פתרון

\int_{0}^{t} 12 e^{2 x} - 12 e^{x} d x

- 12 e^{t} + 6 e^{2 t} + 6

צעדי פתרון

\int_{0}^{t} 12 e^{2 x} - 12 e^{x} d x

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

:הפעל את תכונת הליניאריות

= \int_{0}^{t} 12 e^{2 x} d x - \int_{0}^{t} 12 e^{x} d x

\int_{0}^{t} 12 e^{2 x} d x = 6 (e^{2 t} - 1)

\int_{0}^{t} 12 e^{x} d x = 12 (e^{t} - 1)

= 6 (e^{2 t} - 1) - 12 (e^{t} - 1)

6 (e^{2 t} - 1) - 12 (e^{t} - 1)

פשט את:

- 12 e^{t} + 6 e^{2 t} + 6

= - 12 e^{t} + 6 e^{2 t} + 6

\int_{0}^{1} \frac{e ^{z} + 3}{e ^{z} + 3 z} d z

\int_{3}^{4} t^{2} - 2 t - 3 d t

\int_{0}^{1} 3^{x} d x

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