integral from 0 to 4 of (x-4)^2

Lösung

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

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{0}^{4} x^{2} - 8 x + 16 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

= \int_{0}^{4} x^{2} d x - \int_{0}^{4} 8 x d x + \int_{0}^{4} 16 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 8 x d x = 64

\int_{0}^{4} 16 d x = 64

= \frac{64}{3} - 64 + 64

Vereinfache

= \frac{64}{3}

\frac{\partial}{\partial x} (- sin (y))

x \to 1 - lim (ln (x))

\frac{x d y}{d x} + 2 y = 3

y^{^{''}} + 3 y^{^{'}} = 2 t^{4} + t^{2} e^{- 3 t} + sin (3 t)

y^{^{'}} = x y^{2} + 2 x y