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Beliebt Rechnen >

integral from 0 to 1 of xe^{10x}

Lösung

\int_{0}^{1} x e^{10 x} d x

Lösung

\frac{9 e ^{10} + 1}{100}

+1

Dezimale

1982.39192 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{10 x} d x

Wende U-Substitution an

= \int_{0}^{10} \frac{e ^{u} u}{100} d u

Entferne die Konstante:

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

= \frac{1}{100} \cdot \int_{0}^{10} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{100} [e^{u} u - \int e^{u} d u]_{0}^{10}

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

= \frac{1}{100} [e^{u} u - e^{u}]_{0}^{10}

Berechne die Grenzen:

9 e^{10} + 1

= \frac{1}{100} (9 e^{10} + 1)

Vereinfache

= \frac{9 e ^{10} + 1}{100}

Graph

Beliebte Beispiele

y^{''}-4y^'+2y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} - 4 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

derivative f(x)=x^2[0.2]

d er i v a t i v e f (x) = x^{2} [0.2]

steigung (-10,8),(-15,-7)

s l o p e (- 10, 8), (- 15, - 7)

integral of x/(2-x)

\int \frac{x}{2 - x} d x

derivative (2x^2)/((3-2x)^4)

d er i v a t i v e \frac{2 x ^{2}}{( 3 - 2 x ) ^{4}}