integral from 0 to 3 of 2pi(10-x)(2x)

Lösung

\int_{0}^{3} 2 π (10 - x) (2 x) d x

144 π

Dezimale

452.38934 \dots

Schritte zur Lösung

\int_{0}^{3} 2 π (10 - x) \cdot 2 x d x

Entferne die Konstante:

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

= 2 π 2 \cdot \int_{0}^{3} (10 - x) x d x

Vereinfache

= 4 π \cdot \int_{0}^{3} (10 - x) x d x

Multipliziere aus

(10 - x) x : 10 x - x^{2}

= 4 π \cdot \int_{0}^{3} 10 x - 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

= 4 π (\int_{0}^{3} 10 x d x - \int_{0}^{3} x^{2} d x)

\int_{0}^{3} 10 x d x = 45

\int_{0}^{3} x^{2} d x = 9

= 4 π (45 - 9)

Vereinfache

= 144 π

\int_{0}^{2 π} \frac{1 - cos ( 2 θ )}{2} d θ

\int_{0}^{x} 0.5 x d x

\int_{- 64}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{0}^{3} - 2 x^{3} d x

\int_{0}^{2} (x - 3 y^{2}) d x