integral from 0 to 1 of 9x^8(4-x^9)

Lösung

\int_{0}^{1} 9 x^{8} (4 - x^{9}) d x

\frac{7}{2}

Dezimale

3.5

Schritte zur Lösung

\int_{0}^{1} 9 x^{8} (4 - x^{9}) d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{1} x^{8} (4 - x^{9}) d x

Multipliziere aus

x^{8} (4 - x^{9}) : 4 x^{8} - x^{17}

= 9 \cdot \int_{0}^{1} 4 x^{8} - x^{17} 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

= 9 (\int_{0}^{1} 4 x^{8} d x - \int_{0}^{1} x^{17} d x)

\int_{0}^{1} 4 x^{8} d x = \frac{4}{9}

\int_{0}^{1} x^{17} d x = \frac{1}{18}

= 9 (\frac{4}{9} - \frac{1}{18})

Vereinfache

9 (\frac{4}{9} - \frac{1}{18}) : \frac{7}{2}

= \frac{7}{2}

\int_{4}^{10} b x^{2} d x

\int_{1}^{3} \frac{x ^{2}}{x ^{3} - 27} d x

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

\int_{2}^{3} (x^{3} + x) d x

\int_{x}^{0} e^{- 7 t} d t