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Beliebt Rechnen >

integral from 3 to 5 of e^{-x/2}

Lösung

\int_{3}^{5} e^{- \frac{x}{2}} d x

Lösung

2 (\frac{1}{e ^{\frac{3}{2}}} - \frac{1}{e ^{\frac{5}{2}}})

+1

Dezimale

0.28209 \dots

Schritte zur Lösung

\int_{3}^{5} e^{- \frac{x}{2}} d x

Wende U-Substitution an

= \int_{- \frac{3}{2}}^{- \frac{5}{2}} - 2 e^{u} d u

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

= - \int_{- \frac{5}{2}}^{- \frac{3}{2}} - 2 e^{u} d u

Entferne die Konstante:

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

= - (- 2 \cdot \int_{- \frac{5}{2}}^{- \frac{3}{2}} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- 2 [e^{u}]_{- \frac{5}{2}}^{- \frac{3}{2}})

Vereinfache

= 2 [e^{u}]_{- \frac{5}{2}}^{- \frac{3}{2}}

Berechne die Grenzen:

\frac{1}{e ^{\frac{3}{2}}} - \frac{1}{e ^{\frac{5}{2}}}

= 2 (\frac{1}{e ^{\frac{3}{2}}} - \frac{1}{e ^{\frac{5}{2}}})

Graph

Beliebte Beispiele

integral of sin^3(16x)

\int sin^{3} (16 x) d x

derivative f(x)= 1/((x^3+7)^4)

d er i v a t i v e f (x) = \frac{1}{( x ^{3} + 7 ) ^{4}}

derivative of 2x^3-4x

\frac{d}{d x} (2 x^{3} - 4 x)

derivative 2/(3x^4)

d er i v a t i v e \frac{2}{3 x ^{4}}

sum from n=1 to infinity of n/(5+n^2)

n = 1 \sum \infty \frac{n}{5 + n ^{2}}