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Beliebt Rechnen >

integral from 1 to 2 of ((2sqrt(x-1)))/x

Lösung

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

Lösung

- π + 4

+1

Dezimale

0.85840 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{2 x - 1}{x} d x

Entferne die Konstante:

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

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

Wende U-Substitution an

= 2 \cdot \int_{0}^{1} \frac{2 u ^{2}}{u ^{2} + 1} d u

Entferne die Konstante:

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

= 2 \cdot 2 \cdot \int_{0}^{1} \frac{u ^{2}}{u ^{2} + 1} d u

\frac{u ^{2}}{u ^{2} + 1} = - \frac{1}{u ^{2} + 1} + 1

= 2 \cdot 2 \cdot \int_{0}^{1} - \frac{1}{u ^{2} + 1} + 1 d u

Wende die Summenregel an:

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

= 2 \cdot 2 (- \int_{0}^{1} \frac{1}{u ^{2} + 1} d u + \int_{0}^{1} 1 d u)

\int_{0}^{1} \frac{1}{u ^{2} + 1} d u = \frac{π}{4}

\int_{0}^{1} 1 d u = 1

= 2 \cdot 2 (- \frac{π}{4} + 1)

Vereinfache

2 \cdot 2 (- \frac{π}{4} + 1) : - π + 4

= - π + 4

Graph

Beliebte Beispiele

inverselaplace 1/(s+4)

in v erse l a pl a ce \frac{1}{s + 4}

derivative of 4/((x+1^2))

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

integral of (2/x-3/(x^4))

\int (\frac{2}{x} - \frac{3}{x ^{4}}) d x

steigung y= 2/x

s l o p e y = \frac{2}{x}

integral of x^{1/2}sqrt(1+x^{1/2)}

\int x^{\frac{1}{2}} 1 + x^{\frac{1}{2}} d x