de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 4 of e^{-x}

Lösung

\int_{0}^{4} e^{- x} d x

Lösung

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

+1

Dezimale

0.98168 \dots

Schritte zur Lösung

\int_{0}^{4} e^{- x} d x

Wende U-Substitution an

= \int_{0}^{- 4} - e^{u} d u

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

= - \int_{- 4}^{0} - e^{u} d u

Entferne die Konstante:

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

= - (- \int_{- 4}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= - (- [e^{u}]_{- 4}^{0})

Vereinfache

= [e^{u}]_{- 4}^{0}

Berechne die Grenzen:

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

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of (1/4)^n

n = 1 \sum \infty (\frac{1}{4})^{n}

derivative f(x)=x^4+5x

d er i v a t i v e f (x) = x^{4} + 5 x

derivative of ln(1+x-x)

\frac{d}{d x} (ln (1 + x) - x)

integral of 8we^{7w}

\int 8 w e^{7 w} d w

integral of (8-128x)/(sqrt(1-64x^2))

\int \frac{8 - 128 x}{1 - 64 x ^{2}} d x