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Beliebt Rechnen >

integral from 0 to 15 of 2pix(15x-x^2)

Lösung

\int_{0}^{15} 2 π x (15 x - x^{2}) d x

Lösung

\frac{16875 π}{2}

+1

Dezimale

26507.18801 \dots

Schritte zur Lösung

\int_{0}^{15} 2 π x (15 x - 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}^{15} x (15 x - x^{2}) d x

Multipliziere aus

x (15 x - x^{2}) : 15 x^{2} - x^{3}

= 2 π \cdot \int_{0}^{15} 15 x^{2} - 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}^{15} 15 x^{2} d x - \int_{0}^{15} x^{3} d x)

\int_{0}^{15} 15 x^{2} d x = 16875

\int_{0}^{15} x^{3} d x = \frac{50625}{4}

= 2 π (16875 - \frac{50625}{4})

Vereinfache

2 π (16875 - \frac{50625}{4}) : \frac{16875 π}{2}

= \frac{16875 π}{2}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(ln((2xy)/(5z)))

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

integral of-9/(x^{10)}

\int - \frac{9}{x ^{10}} d x

(\partial)/(\partial x)(u)

\frac{\partial}{\partial x} (u)

derivative of 4pix

\frac{d}{d x} (4 π x)

limit as x approaches-2 of 1/(2x)

x \to - 2 lim (\frac{1}{2 x})