integral from 1/2 to 1 of 4/9 x(5-x^2)

Lösung

\int_{\frac{1}{2}}^{1} \frac{4}{9} x (5 - x^{2}) d x

\frac{35}{48}

Dezimale

0.72916 \dots

Schritte zur Lösung

\int_{\frac{1}{2}}^{1} \frac{4}{9} x (5 - x^{2}) d x

Entferne die Konstante:

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

= \frac{4}{9} \cdot \int_{\frac{1}{2}}^{1} x (5 - x^{2}) d x

Multipliziere aus

x (5 - x^{2}) : 5 x - x^{3}

= \frac{4}{9} \cdot \int_{\frac{1}{2}}^{1} 5 x - x^{3} 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{4}{9} (\int_{\frac{1}{2}}^{1} 5 x d x - \int_{\frac{1}{2}}^{1} x^{3} d x)

\int_{\frac{1}{2}}^{1} 5 x d x = \frac{15}{8}

\int_{\frac{1}{2}}^{1} x^{3} d x = \frac{15}{64}

= \frac{4}{9} (\frac{15}{8} - \frac{15}{64})

Vereinfache

\frac{4}{9} (\frac{15}{8} - \frac{15}{64}) : \frac{35}{48}

= \frac{35}{48}

d er i v a t i v e \frac{t - t}{t ^{\frac{1}{7}}}

\frac{d}{d x} (x sin (y - z))

d er i v a t i v e y = (\frac{3 x ^{2}}{2 x + 4})^{3}

in v erse l a pl a ce \frac{5}{s ( s ^{2} + 5 ^{2} )}

l a pl a ce t r an s f or m f (t) = 2 (1 - e^{- 5 t})