integral from 0 to 1 of 5e^{5sqrt(x)}

Lösung

\int_{0}^{1} 5 e^{5 x} d x

\frac{2 ( 4 e ^{5} + 1 )}{5}

Dezimale

237.86105 \dots

Schritte zur Lösung

\int_{0}^{1} 5 e^{5 x} d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{1} e^{5 x} d x

Wende U-Substitution an

= 5 \cdot \int_{0}^{5} \frac{2 e ^{u} u}{25} d u

Entferne die Konstante:

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

= 5 \cdot \frac{2}{25} \cdot \int_{0}^{5} e^{u} u d u

Wende die partielle Integration an

= 5 \cdot \frac{2}{25} [e^{u} u - \int e^{u} d u]_{0}^{5}

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

= 5 \cdot \frac{2}{25} [e^{u} u - e^{u}]_{0}^{5}

Vereinfache

5 \cdot \frac{2}{25} [e^{u} u - e^{u}]_{0}^{5} : \frac{2}{5} [e^{u} u - e^{u}]_{0}^{5}

= \frac{2}{5} [e^{u} u - e^{u}]_{0}^{5}

Berechne die Grenzen:

4 e^{5} + 1

= \frac{2}{5} (4 e^{5} + 1)

Vereinfache

= \frac{2 ( 4 e ^{5} + 1 )}{5}

\frac{d}{d x} (\frac{9 x}{x})

x \to 0 + lim (x^{x^{8}})

\int 36 x^{3} (3 x^{4} + 3)^{5} d x

y \to 0 lim (\frac{0}{y})

t an g e n t f (x) = (x^{2} - 3) (x^{3} - 2 x), at x = - 2