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Beliebt Rechnen >

integral from-1 to 5 of (3e^{-x})^2

Lösung

\int_{- 1}^{5} (3 e^{- x})^{2} d x

Lösung

- \frac{9}{2 e ^{10}} + \frac{9 e ^{2}}{2}

+1

Dezimale

33.25054 \dots

Schritte zur Lösung

\int_{- 1}^{5} (3 e^{- x})^{2} d x

Wende die partielle Integration an

= [9 e^{- 2 x} x - \int - 18 e^{- 2 x} x d x]_{- 1}^{5}

\int - 18 e^{- 2 x} x d x = 9 e^{- 2 x} x + \frac{9}{2} e^{- 2 x}

= [9 e^{- 2 x} x - (9 e^{- 2 x} x + \frac{9}{2} e^{- 2 x})]_{- 1}^{5}

Vereinfache

= [- \frac{9}{2} e^{- 2 x}]_{- 1}^{5}

Berechne die Grenzen:

- \frac{9}{2 e ^{10}} + e^{2} \frac{9}{2}

= - \frac{9}{2 e ^{10}} + e^{2} \frac{9}{2}

Vereinfache

= - \frac{9}{2 e ^{10}} + \frac{9 e ^{2}}{2}

Graph

Beliebte Beispiele

integral of (2x)/(\sqrt[3]{9-x^2)}

\int \frac{2 x}{3 9 - x ^{2}} d x

limit as x approaches 1-of x^{(1/(1-x))}

x \to 1 - lim (x^{(\frac{1}{1 - x})})

d/(d{z)}({x}{y}e^{{z}})

\frac{d}{d z} (x y e^{z})

derivative f(x)=ln(sqrt(x)+9)

d er i v a t i v e f (x) = ln (x + 9)

(dy)/(dx)=e^{3x}+2y

\frac{d y}{d x} = e^{3 x} + 2 y