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Beliebt Rechnen >

integral from 0 to 5 of xsqrt(5-x)

Lösung

\int_{0}^{5} x 5 - x d x

Lösung

- 105 + \frac{50 5}{3}

+1

Dezimale

14.90711 \dots

Schritte zur Lösung

\int_{0}^{5} x 5 - x d x

Wende U-Substitution an

= \int_{5}^{0} - (- u + 5) u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{5} - (- u + 5) u d u

Entferne die Konstante:

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

= - (- \int_{0}^{5} (- u + 5) u d u)

Multipliziere aus

(- u + 5) u : - u^{\frac{3}{2}} + 5 u

= - (- \int_{0}^{5} - u^{\frac{3}{2}} + 5 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

= - (- (- \int_{0}^{5} u^{\frac{3}{2}} d u + \int_{0}^{5} 5 u d u))

\int_{0}^{5} u^{\frac{3}{2}} d u = 105

\int_{0}^{5} 5 u d u = \frac{50 5}{3}

= - (- (- 105 + \frac{50 5}{3}))

Vereinfache

= - 105 + \frac{50 5}{3}

Graph

Beliebte Beispiele

x^2y^{''}+2xy^'-6y=0,y(1)=0

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0, y (1) = 0

derivative of e^{5x+2x^2}

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

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

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

integral of sec(t)(sec(t)+tan(t))

\int sec (t) (sec (t) + tan (t)) d t

fläche y=3x-x^2,y=0

a re a y = 3 x - x^{2}, y = 0