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Beliebt Rechnen >

integral from 0 to 5 of 2pi(7-x)(25-x^2)

Lösung

\int_{0}^{5} 2 π (7 - x) (25 - x^{2}) d x

Lösung

\frac{5125 π}{6}

+1

Dezimale

2683.44372 \dots

Schritte zur Lösung

\int_{0}^{5} 2 π (7 - x) (25 - x^{2}) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{5} (7 - x) (25 - x^{2}) d x

Multipliziere aus

(7 - x) (25 - x^{2}) : 175 - 7 x^{2} - 25 x + x^{3}

= 2 π \cdot \int_{0}^{5} 175 - 7 x^{2} - 25 x + x^{3} 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

= 2 π (\int_{0}^{5} 175 d x - \int_{0}^{5} 7 x^{2} d x - \int_{0}^{5} 25 x d x + \int_{0}^{5} x^{3} d x)

\int_{0}^{5} 175 d x = 875

\int_{0}^{5} 7 x^{2} d x = \frac{875}{3}

\int_{0}^{5} 25 x d x = \frac{625}{2}

\int_{0}^{5} x^{3} d x = \frac{625}{4}

= 2 π (875 - \frac{875}{3} - \frac{625}{2} + \frac{625}{4})

Vereinfache

2 π (875 - \frac{875}{3} - \frac{625}{2} + \frac{625}{4}) : \frac{5125 π}{6}

= \frac{5125 π}{6}

Graph

Beliebte Beispiele

integral of-e^{2x}cos(2x)

\int - e^{2 x} cos (2 x) d x

derivative y=3^x+1

d er i v a t i v e y = 3^{x} + 1

derivative of (x^4-3x^3-6x^2-3x+2/x)

\frac{d}{d x} (\frac{x ^{4} - 3 x ^{3} - 6 x ^{2} - 3 x + 2}{x})

tangent f(x)= x/((2x-1)^6),\at x=1

t an g e n t f (x) = \frac{x}{( 2 x - 1 ) ^{6}}, at x = 1

(dy)/(dx)+3y+5=0

\frac{d y}{d x} + 3 y + 5 = 0