integral from 1 to 2 of 1/8 (2+2x-x^2)

Lösung

\int_{1}^{2} \frac{1}{8} (2 + 2 x - x^{2}) d x

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{1}{8} (2 + 2 x - x^{2}) d x

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{1}^{2} 2 + 2 x - x^{2} 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}{8} (\int_{1}^{2} 2 d x + \int_{1}^{2} 2 x d x - \int_{1}^{2} x^{2} d x)

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

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

= \frac{1}{8} (2 + 3 - \frac{7}{3})

Vereinfache

\frac{1}{8} (2 + 3 - \frac{7}{3}) : \frac{1}{3}

= \frac{1}{3}

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

\int_{0}^{\frac{4}{3}} π (4 - 3 x)^{2} d x

z \to \frac{1}{2} lim (\frac{3 z + 1}{2 z - 5})

\frac{\partial}{\partial y} (8 x e^{x^{2} + y^{2}})

d er i v a t i v e f (x) = 4 x