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

Lösung

\int_{0}^{5} π (25 - 25 x^{2}) d x

- π \frac{2750}{3}

Dezimale

- 2879.79326 \dots

Schritte zur Lösung

\int_{0}^{5} π (25 - 25 x^{2}) d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{5} 25 - 25 x^{2} 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

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

\int_{0}^{5} 25 d x = 125

\int_{0}^{5} 25 x^{2} d x = \frac{3125}{3}

= π (125 - \frac{3125}{3})

Vereinfache

π (125 - \frac{3125}{3}) : - π \frac{2750}{3}

= - π \frac{2750}{3}

x \to 5 lim (3 x^{2} + 5)

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

\frac{d}{d x} (\frac{c ^{6} - x ^{6}}{c ^{6} + x ^{6}})

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\int_{0}^{2} π (x^{3} - 8)^{2} d x