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

Lösung

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

\frac{512}{15}

Dezimale

34.13333 \dots

Schritte zur Lösung

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

Multipliziere aus

(4 x - x^{2})^{2} : 16 x^{2} - 8 x^{3} + x^{4}

= \int_{0}^{4} 16 x^{2} - 8 x^{3} + x^{4} 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} 16 x^{2} d x - \int_{0}^{4} 8 x^{3} d x + \int_{0}^{4} x^{4} d x

\int_{0}^{4} 16 x^{2} d x = \frac{1024}{3}

\int_{0}^{4} 8 x^{3} d x = 512

\int_{0}^{4} x^{4} d x = \frac{1024}{5}

= \frac{1024}{3} - 512 + \frac{1024}{5}

Vereinfache

\frac{1024}{3} - 512 + \frac{1024}{5} : \frac{512}{15}

= \frac{512}{15}

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

\frac{d}{d x} (x lo g_{e} (2 x))

y^{''} (t)

t an g e n t f (x) = 3 - 2 x e^{x}, at x = 0

t an g e n t f (x) = (10 x - 4)^{\frac{1}{2}}, at x = 2