integral from 1/4 to 1/2 of 2/5 (x+2)

Lösung

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{2}{5} (x + 2) d x

\frac{19}{80}

Dezimale

0.2375

Schritte zur Lösung

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{2}{5} (x + 2) d x

Entferne die Konstante:

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

= \frac{2}{5} \cdot \int_{\frac{1}{4}}^{\frac{1}{2}} 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{2}{5} (\int_{\frac{1}{4}}^{\frac{1}{2}} x d x + \int_{\frac{1}{4}}^{\frac{1}{2}} 2 d x)

\int_{\frac{1}{4}}^{\frac{1}{2}} x d x = \frac{3}{32}

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

= \frac{2}{5} (\frac{3}{32} + \frac{1}{2})

Vereinfache

\frac{2}{5} (\frac{3}{32} + \frac{1}{2}) : \frac{19}{80}

= \frac{19}{80}

\int_{2}^{4} 3 x ln (x) d x

\int_{y}^{8 - y^{2}} 1 d x

\int_{2}^{3} \frac{x}{8} d x

\int_{0}^{1} x^{4} + 1 d x

\int_{0}^{5} 11 + x^{2} d x