integral from 0 to 1 of pi(x-x^{12})

Lösung

\int_{0}^{1} π (x - x^{12}) d x

π \frac{11}{26}

Dezimale

1.32913 \dots

Schritte zur Lösung

\int_{0}^{1} π (x - x^{12}) d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{1} x - x^{12} 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

= π (\int_{0}^{1} x d x - \int_{0}^{1} x^{12} d x)

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} x^{12} d x = \frac{1}{13}

= π (\frac{1}{2} - \frac{1}{13})

Füge

\frac{1}{2} - \frac{1}{13}

zusammen:

\frac{11}{26}

= π \frac{11}{26}

\int \frac{3 x ^{2} - x + 2 e}{x ^{2}} d x

\int_{2}^{3} π (x + x^{2})^{2} d x

t an g e n t f (x) = \frac{11}{2} - x^{2}, at x = - 2

\int cos (2 x - 3) d x

k = 0 \sum \infty (\frac{1}{2})^{2 k + 1}