integral from 1 to 5 of (3t)/(e^{2t)}

Lösung

\int_{1}^{5} \frac{3 t}{e ^{2 t}} d t

3 (- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}})

Dezimale

0.30412 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{3 t}{e ^{2 t}} d t

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{5} \frac{t}{e ^{2 t}} d t

Wende die partielle Integration an

= 3 [- \frac{1}{2} e^{- 2 t} t - \int - \frac{1}{2} e^{- 2 t} d t]_{1}^{5}

\int - \frac{1}{2} e^{- 2 t} d t = \frac{1}{4} e^{- 2 t}

= 3 [- \frac{1}{2} e^{- 2 t} t - \frac{1}{4} e^{- 2 t}]_{1}^{5}

Berechne die Grenzen:

- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}}

= 3 (- \frac{11}{4 e ^{10}} + \frac{3}{4 e ^{2}})

\int_{0}^{4} e^{(x - 2)^{4}} d x

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