integral from-3 to 0 of (6x-e^x)

Lösung

\int_{- 3}^{0} (6 x - e^{x}) d x

\frac{1}{e ^{3}} - 28

Dezimale

- 27.95021 \dots

Schritte zur Lösung

\int_{- 3}^{0} 6 x - e^{x} 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_{- 3}^{0} 6 x d x - \int_{- 3}^{0} e^{x} d x

\int_{- 3}^{0} 6 x d x = - 27

\int_{- 3}^{0} e^{x} d x = 1 - \frac{1}{e ^{3}}

= - 27 - (1 - \frac{1}{e ^{3}})

Vereinfache

= \frac{1}{e ^{3}} - 28

\int_{0}^{4} \frac{1}{64 t ^{2} + 25} d t

\int_{1}^{2} \frac{64}{3} - 8 y^{2} d y

\int_{0}^{\frac{1}{2}} 4 x e^{2 x} d x

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\int_{0}^{\infty} e^{- 3} d x