intégrale de 0 a 1 de x(x+1)^{10}

Solution

\int_{0}^{1} x (x + 1)^{10} d x

\frac{6827}{44}

Décimale

155.15909 \dots

étapes des solutions

\int_{0}^{1} x (x + 1)^{10} d x

Appliquer l'intégration par subsitution

= \int_{1}^{2} (u - 1) u^{10} d u

Développer

(u - 1) u^{10} : u^{11} - u^{10}

= \int_{1}^{2} u^{11} - u^{10} d u

Appliquer la règle de la somme:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} u^{11} d u - \int_{1}^{2} u^{10} d u

\int_{1}^{2} u^{11} d u = \frac{1365}{4}

\int_{1}^{2} u^{10} d u = \frac{2047}{11}

= \frac{1365}{4} - \frac{2047}{11}

Simplifier

\frac{1365}{4} - \frac{2047}{11} : \frac{6827}{44}

= \frac{6827}{44}