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Beliebt Rechnen >

integral from 0 to 1 of xsqrt(5x+4)

Lösung

\int_{0}^{1} x 5 x + 4 d x

Lösung

\frac{506}{375}

+1

Dezimale

1.34933 \dots

Schritte zur Lösung

\int_{0}^{1} x 5 x + 4 d x

Wende U-Substitution an

= \int_{4}^{9} \frac{u ( u - 4 )}{25} d u

Entferne die Konstante:

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

= \frac{1}{25} \cdot \int_{4}^{9} u (u - 4) d u

Multipliziere aus

u (u - 4) : u^{\frac{3}{2}} - 4 u

= \frac{1}{25} \cdot \int_{4}^{9} u^{\frac{3}{2}} - 4 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{1}{25} (\int_{4}^{9} u^{\frac{3}{2}} d u - \int_{4}^{9} 4 u d u)

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 4 u d u = \frac{152}{3}

= \frac{1}{25} (\frac{422}{5} - \frac{152}{3})

Vereinfache

\frac{1}{25} (\frac{422}{5} - \frac{152}{3}) : \frac{506}{375}

= \frac{506}{375}

Graph

Beliebte Beispiele

integral of x^2+sin(x)

\int x^{2} + sin (x) d x

integral of ((x^3))/(sqrt(4+x^2))

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

derivative of xn(x)

\frac{d}{d x} (x n (x))

derivative (-4)/((7x^5+6)^6)

d er i v a t i v e \frac{- 4}{( 7 x ^{5} + 6 ) ^{6}}

laplacetransform 10t

l a pl a ce t r an s f or m 10 t