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Beliebt Rechnen >

integral from 0 to 1 of 2pi(2-y)(7-7y^2)

Lösung

\int_{0}^{1} 2 π (2 - y) (7 - 7 y^{2}) d y

Lösung

\frac{91 π}{6}

+1

Dezimale

47.64748 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π (2 - y) (7 - 7 y^{2}) d y

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} (2 - y) (7 - 7 y^{2}) d y

Multipliziere aus

(2 - y) (7 - 7 y^{2}) : 14 - 14 y^{2} - 7 y + 7 y^{3}

= 2 π \cdot \int_{0}^{1} 14 - 14 y^{2} - 7 y + 7 y^{3} d y

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}^{1} 14 d y - \int_{0}^{1} 14 y^{2} d y - \int_{0}^{1} 7 y d y + \int_{0}^{1} 7 y^{3} d y)

\int_{0}^{1} 14 d y = 14

\int_{0}^{1} 14 y^{2} d y = \frac{14}{3}

\int_{0}^{1} 7 y d y = \frac{7}{2}

\int_{0}^{1} 7 y^{3} d y = \frac{7}{4}

= 2 π (14 - \frac{14}{3} - \frac{7}{2} + \frac{7}{4})

Vereinfache

2 π (14 - \frac{14}{3} - \frac{7}{2} + \frac{7}{4}) : \frac{91 π}{6}

= \frac{91 π}{6}

Graph

Beliebte Beispiele

inverselaplace 3/(4s)

in v erse l a pl a ce \frac{3}{4 s}

derivative of sec^2(x^3)

\frac{d}{d x} (sec^{2} (x^{3}))

limit as x approaches 2 of-x+7

x \to 2 lim (- x + 7)

integral of (x^3)/(x^4+6)

\int \frac{x ^{3}}{x ^{4} + 6} d x

tangent f(x)=ln(x^7),(1,0)

t an g e n t f (x) = ln (x^{7}), (1, 0)