integral from 1 to 4 of 6e^{sqrt(x)}

Lösung

\int_{1}^{4} 6 e^{x} d x

12 e^{2}

Dezimale

88.66867 \dots

Schritte zur Lösung

\int_{1}^{4} 6 e^{x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{4} e^{x} d x

Wende U-Substitution an

= 6 \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

= 6 \cdot 2 \cdot \int_{1}^{2} e^{u} u d u

Wende die partielle Integration an

= 6 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

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

Vereinfache

= 12 [e^{u} u - e^{u}]_{1}^{2}

Berechne die Grenzen:

e^{2}

= 12 e^{2}

cr i t i c a l f (x, y) = (x)^{2} + (y)^{4}

x \to 3 + lim (\frac{1}{∣ x - 3 ∣})

y \to 0 lim (\frac{y ^{2}}{y ^{4}})

d er i v a t i v e f (x) = e^{x} - x^{7}

x \to 1 lim (\frac{x ^{2} - 9}{x - 3})