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Beliebt Rechnen >

integral from 0 to ln(2) of e^{-x}

Lösung

\int_{0}^{l n (2)} e^{- x} d x

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{l n (2)} e^{- x} d x

Wende U-Substitution an

= \int_{0}^{- l n (2)} - e^{u} d u

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

= - \int_{- l n (2)}^{0} - e^{u} d u

Entferne die Konstante:

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

= - (- \int_{- l n (2)}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- [e^{u}]_{- l n (2)}^{0})

Vereinfache

= [e^{u}]_{- l n (2)}^{0}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{2}

Graph

Beliebte Beispiele

(dy)/(dx)=(sec(y))/((x-1)^2)

\frac{d y}{d x} = \frac{sec ( y )}{( x - 1 ) ^{2}}

integral of (-x^2-2x)

\int (- x^{2} - 2 x) d x

fläche y=sqrt(x),y= 1/2 x,x=9

a re a y = x, y = \frac{1}{2} x, x = 9

derivative of 1/(x^2+2x+1)

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

tangent y=(s-4)(s^2-3),(1,6)

t an g e n t y = (s - 4) (s^{2} - 3), (1, 6)