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Beliebt Rechnen >

integral from 1 to 4 of (x+1)/(2sqrt(x))

Lösung

\int_{1}^{4} \frac{x + 1}{2 x} d x

Lösung

\frac{10}{3}

+1

Dezimale

3.33333 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{x + 1}{2 x} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{4} \frac{x + 1}{x} d x

Multipliziere aus

\frac{x + 1}{x} : x + \frac{1}{x}

= \frac{1}{2} \cdot \int_{1}^{4} x + \frac{1}{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{1}{2} (\int_{1}^{4} x d x + \int_{1}^{4} \frac{1}{x} d x)

\int_{1}^{4} x d x = \frac{14}{3}

\int_{1}^{4} \frac{1}{x} d x = 2

= \frac{1}{2} (\frac{14}{3} + 2)

Vereinfache

\frac{1}{2} (\frac{14}{3} + 2) : \frac{10}{3}

= \frac{10}{3}

Graph

Beliebte Beispiele

integral from 0 to 1 of x^e

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

integral from 2 to 7 of 4

\int_{2}^{7} 4 d x

integral from 6 to 11 of 3xsqrt(x-2)

\int_{6}^{11} 3 x x - 2 d x

integral from-10 to 10 of |x|

\int_{- 10}^{10} ∣ x ∣ d x

integral from 0 to pi of (1-cos(x))^2

\int_{0}^{π} (1 - cos (x))^{2} d x