integral from 6 to 11 of 3xsqrt(x-2)

Lösung

\int_{6}^{11} 3 x x - 2 d x

\frac{1646}{5}

Dezimale

329.2

Schritte zur Lösung

\int_{6}^{11} 3 x x - 2 d x

Entferne die Konstante:

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

= 3 \cdot \int_{6}^{11} x x - 2 d x

Wende U-Substitution an

= 3 \cdot \int_{4}^{9} (u + 2) u d u

Multipliziere aus

(u + 2) u : u^{\frac{3}{2}} + 2 u

= 3 \cdot \int_{4}^{9} u^{\frac{3}{2}} + 2 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 3 (\int_{4}^{9} u^{\frac{3}{2}} d u + \int_{4}^{9} 2 u d u)

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 2 u d u = \frac{76}{3}

= 3 (\frac{422}{5} + \frac{76}{3})

Vereinfache

3 (\frac{422}{5} + \frac{76}{3}) : \frac{1646}{5}

= \frac{1646}{5}

\int_{- 10}^{10} ∣ x ∣ d x

\int_{0}^{π} (1 - cos (x))^{2} d x

\int_{0}^{6} 4 x d x

\int_{- 3}^{5} (2 x + 15 - x^{2}) d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos^{6} (θ) d θ