integral from-1 to 1 of 1/2 (1-x^4)

Lösung

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

\frac{4}{5}

Dezimale

0.8

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 1}^{1} 1 - 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

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

\int_{- 1}^{1} 1 d x = 2

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

= \frac{1}{2} (2 - \frac{2}{5})

Vereinfache

\frac{1}{2} (2 - \frac{2}{5}) : \frac{4}{5}

= \frac{4}{5}

\int \frac{x ^{3} + 5 x + 1}{x ^{2} + 5} d x

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

\frac{\partial}{\partial y} (y - ln (x^{2} + y^{2}))

d er i v a t i v e y = \frac{3}{x ^{2} - 1}

x \to 0 + lim (6 (cot (x) - \frac{1}{x}))