integral from 2 to 4 of (1-e^{-x})

Lösung

\int_{2}^{4} (1 - e^{- x}) d x

2 - \frac{1}{e ^{2}} + \frac{1}{e ^{4}}

Dezimale

1.88298 \dots

Schritte zur Lösung

\int_{2}^{4} 1 - e^{- x} d x

Wende U-Substitution an

= \int_{- 2}^{- 4} - 1 + e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 4}^{- 2} - 1 + e^{u} d u

Wende die Summenregel an:

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

= - (- \int_{- 4}^{- 2} 1 d u + \int_{- 4}^{- 2} e^{u} d u)

\int_{- 4}^{- 2} 1 d u = 2

\int_{- 4}^{- 2} e^{u} d u = \frac{1}{e ^{2}} - \frac{1}{e ^{4}}

= - (- 2 + \frac{1}{e ^{2}} - \frac{1}{e ^{4}})

Vereinfache

= 2 - \frac{1}{e ^{2}} + \frac{1}{e ^{4}}

\int_{0}^{3} 3 x (1 + 3 x^{2})^{2} d x

\int_{y}^{\infty} x e^{- x} d x

\int_{1}^{2} 6 x^{2} - 3 x d x

\int_{0}^{4} \frac{x}{4 + 2 x ^{2}} d x

\int_{7}^{10} x d x