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

Lösung

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

\frac{4}{15}

Dezimale

0.26666 \dots

Schritte zur Lösung

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

Multipliziere aus

x^{2} (1 - x^{2}) : x^{2} - x^{4}

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

\int_{- 1}^{1} x^{2} d x = \frac{2}{3}

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

= \frac{2}{3} - \frac{2}{5}

Vereinfache

\frac{2}{3} - \frac{2}{5} : \frac{4}{15}

= \frac{4}{15}

\frac{\partial}{\partial x} (5 y cos (6 x))

\int x^{2} ln (x^{2} + 1) d x

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

x y^{^{'}} + y + x = 0, y (1) = 1

\frac{\partial}{\partial x} (ln (x^{5} - y^{4}))