integral from 1 to 4 of 3e^{sqrt(x)}

Lösung

\int_{1}^{4} 3 e^{x} d x

6 e^{2}

Dezimale

44.33433 \dots

Schritte zur Lösung

\int_{1}^{4} 3 e^{x} d x

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{4} e^{x} d x

Wende U-Substitution an

= 3 \cdot \int_{1}^{2} e^{u} \cdot 2 u d u

Entferne die Konstante:

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

= 3 \cdot 2 \cdot \int_{1}^{2} e^{u} u d u

Wende die partielle Integration an

= 3 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 3 \cdot 2 [e^{u} u - e^{u}]_{1}^{2}

Vereinfache

= 6 [e^{u} u - e^{u}]_{1}^{2}

Berechne die Grenzen:

e^{2}

= 6 e^{2}

\frac{d}{d x} (tan (π))

a re a x = 1, y = 6 x (2 - x^{2})^{2}

x \to - 4 - lim (\frac{- 4 x ^{3}}{4 + x})

x \to a + lim (x^{n})

\int \frac{x ^{6} + 4 x ^{3} + 4}{x ^{3} - 4 x ^{2}} d x