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Beliebt Rechnen >

integral from 1 to 2 of 2/5 x(x+1)

Lösung

\int_{1}^{2} \frac{2}{5} x (x + 1) d x

Lösung

\frac{23}{15}

+1

Dezimale

1.53333 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{2}{5} x (x + 1) d x

Entferne die Konstante:

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

= \frac{2}{5} \cdot \int_{1}^{2} x (x + 1) d x

Multipliziere aus

x (x + 1) : x^{2} + x

= \frac{2}{5} \cdot \int_{1}^{2} x^{2} + x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{2}{5} (\int_{1}^{2} x^{2} d x + \int_{1}^{2} x d x)

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} x d x = \frac{3}{2}

= \frac{2}{5} (\frac{7}{3} + \frac{3}{2})

Vereinfache

\frac{2}{5} (\frac{7}{3} + \frac{3}{2}) : \frac{23}{15}

= \frac{23}{15}

Graph

Beliebte Beispiele

limit as x approaches 15 of (x^2)/5-3/x

x \to 15 lim (\frac{x ^{2}}{5} - \frac{3}{x})

derivative of (x^2/(1+2x))

\frac{d}{d x} (\frac{x ^{2}}{1 + 2 x})

y^{''}+16y=16sec(4t)

y^{^{''}} + 16 y = 16 sec (4 t)

limit as x approaches 0 of cot(x)arcsin(x)

x \to 0 lim (cot (x) arcsin (x))

integral of 1/(7-2x)

\int \frac{1}{7 - 2 x} d x