integral from 2 to 4 of x^2((2x-3))/6

Lösung

\int_{2}^{4} x^{2} \frac{( 2 x - 3 )}{6} d x

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{2}^{4} x^{2} \frac{2 x - 3}{6} d x

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{2}^{4} x^{2} (2 x - 3) d x

Multipliziere aus

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

= \frac{1}{6} \cdot \int_{2}^{4} 2 x^{3} - 3 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

= \frac{1}{6} (\int_{2}^{4} 2 x^{3} d x - \int_{2}^{4} 3 x^{2} d x)

\int_{2}^{4} 2 x^{3} d x = 120

\int_{2}^{4} 3 x^{2} d x = 56

= \frac{1}{6} (120 - 56)

Vereinfache

\frac{1}{6} (120 - 56) : \frac{32}{3}

= \frac{32}{3}

x \to 2 + lim (a x^{2} - b x + 3)

\int_{0}^{2} \int_{0}^{1} x y e^{x y^{2}} d y d x

\int \frac{1}{x ^{2} + 11} d x

\frac{d P}{d t} = (\frac{P}{5}) (lo g_{e} (\frac{3000}{P}))

\frac{\partial}{\partial x} (6 y^{5} sin (3 x))