integral from 0 to 30 of 4x(30-x)

Lösung

\int_{0}^{30} 4 x (30 - x) d x

18000

Schritte zur Lösung

\int_{0}^{30} 4 x (30 - x) d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{30} x (30 - x) d x

Multipliziere aus

x (30 - x) : 30 x - x^{2}

= 4 \cdot \int_{0}^{30} 30 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 (\int_{0}^{30} 30 x d x - \int_{0}^{30} x^{2} d x)

\int_{0}^{30} 30 x d x = 13500

\int_{0}^{30} x^{2} d x = 9000

= 4 (13500 - 9000)

Vereinfache

= 18000

\frac{\partial}{\partial x} (x^{3} e^{4 x y})

y^{^{'}} = \frac{y}{t} - \frac{1}{\frac{y}{t}}

t an g e n t f (x) = x + \frac{2}{x}, at x = 2

\int \frac{50}{x ^{0.25}} d x

\frac{d}{d y} (x e^{x - y})