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 1 of e^{-0.1x}

Lösung

\int_{0}^{1} e^{- 0.1 x} d x

Lösung

0.95162 \dots

Schritte zur Lösung

\int_{0}^{1} e^{- 0.1 x} d x

Wende U-Substitution an

= \int_{0}^{- 0.1} - \frac{1}{0.1} e^{u} d u

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

= - \int_{- 0.1}^{0} - \frac{1}{0.1} e^{u} d u

Entferne die Konstante:

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

= - (- \frac{1}{0.1} \cdot \int_{- 0.1}^{0} e^{u} d u)

Vereinfache

= - (- 10 \cdot \int_{- 0.1}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- 10 [e^{u}]_{- 0.1}^{0})

Vereinfache

= 10 [e^{u}]_{- 0.1}^{0}

Berechne die Grenzen:

0.09516 \dots

= 10 \cdot 0.09516 \dots

Vereinfache

= 0.95162 \dots

Graph

Beliebte Beispiele

derivative y=e^2x

d er i v a t i v e y = e^{2} x

d/(d{z)}(sqrt({x)^2+{y}^2+{z}^2})

\frac{d}{d z} (x^{2} + y^{2} + z^{2})

integral of ((x^3+1)^2)/(x^2)

\int \frac{( x ^{3} + 1 ) ^{2}}{x ^{2}} d x

derivative of y=sec(2x)

\frac{d}{d x} y = sec (2 x)

tangent f(x)=2xsqrt(x-2),\at x=3

t an g e n t f (x) = 2 x x - 2, at x = 3