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Beliebt Rechnen >

integral from 0 to 3 of 3/2 xsqrt(x+1)

Lösung

\int_{0}^{3} \frac{3}{2} x x + 1 d x

Lösung

\frac{58}{5}

+1

Dezimale

11.6

Schritte zur Lösung

\int_{0}^{3} \frac{3}{2} x x + 1 d x

Entferne die Konstante:

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

= \frac{3}{2} \cdot \int_{0}^{3} x x + 1 d x

Wende U-Substitution an

= \frac{3}{2} \cdot \int_{1}^{4} (u - 1) u d u

Multipliziere aus

(u - 1) u : u^{\frac{3}{2}} - u

= \frac{3}{2} \cdot \int_{1}^{4} u^{\frac{3}{2}} - u 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

= \frac{3}{2} (\int_{1}^{4} u^{\frac{3}{2}} d u - \int_{1}^{4} u d u)

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

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

= \frac{3}{2} (\frac{62}{5} - \frac{14}{3})

Vereinfache

\frac{3}{2} (\frac{62}{5} - \frac{14}{3}) : \frac{58}{5}

= \frac{58}{5}

Graph

Beliebte Beispiele

integral from 2 to 8 of-sqrt(x/2)

\int_{2}^{8} - \frac{x}{2} d x

integral of (cos(ln(9t)))/t

\int \frac{cos ( ln ( 9 t ) )}{t} d t

derivative of e^{2cos(3x})

\frac{d}{d x} (e^{2 c o s (3 x)})

y^{''}+4y^'+4y=0,y(0)=2,y^'(0)=-9

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 9

fläche y^2-6x=1,x-y=1

a re a y^{2} - 6 x = 1, x - y = 1