integral from 0 to 1 of (1-x^7)^2

Lösung

\int_{0}^{1} (1 - x^{7})^{2} d x

\frac{49}{60}

Dezimale

0.81666 \dots

Schritte zur Lösung

\int_{0}^{1} (1 - x^{7})^{2} d x

Multipliziere aus

(1 - x^{7})^{2} : 1 - 2 x^{7} + x^{14}

= \int_{0}^{1} 1 - 2 x^{7} + x^{14} 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}^{1} 1 d x - \int_{0}^{1} 2 x^{7} d x + \int_{0}^{1} x^{14} d x

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} 2 x^{7} d x = \frac{1}{4}

\int_{0}^{1} x^{14} d x = \frac{1}{15}

= 1 - \frac{1}{4} + \frac{1}{15}

Vereinfache

1 - \frac{1}{4} + \frac{1}{15} : \frac{49}{60}

= \frac{49}{60}

d er i v a t i v e x^{3} - 2 x^{2} - 4 x + 6

y^{^{''}} - 2 y^{^{'}} = x + 2 e^{x}, y (0) = 18, y^{^{'}} (0) = \frac{31}{4}

\frac{d}{d x} (2 cos (x) + 3 sin (x))

in v erse l a pl a ce \frac{s + 3}{s ^{2} + 2 s + 2}

t an g e n t 5 x^{2} + 8 x - 8