integral from 1 to 2 of x(2-x)^{99}

Lösung

\int_{1}^{2} x (2 - x)^{99} d x

\frac{51}{5050}

Dezimale

0.01009 \dots

Schritte zur Lösung

\int_{1}^{2} x (2 - x)^{99} d x

Wende die partielle Integration an

= [- \frac{1}{100} x (2 - x)^{100} - \int - \frac{1}{100} (2 - x)^{100} d x]_{1}^{2}

\int - \frac{1}{100} (2 - x)^{100} d x = \frac{1}{10100} (2 - x)^{101}

= [- \frac{1}{100} x (2 - x)^{100} - \frac{1}{10100} (2 - x)^{101}]_{1}^{2}

Vereinfache

[- \frac{1}{100} x (2 - x)^{100} - \frac{1}{10100} (2 - x)^{101}]_{1}^{2} : [- \frac{1}{5050} (- x + 2)^{100} (50 x + 1)]_{1}^{2}

= [- \frac{1}{5050} (- x + 2)^{100} (50 x + 1)]_{1}^{2}

Berechne die Grenzen:

\frac{51}{5050}

= \frac{51}{5050}

\int_{- 2}^{2} 9 - \frac{9}{4} x^{2} d x

\int_{2}^{\infty} \frac{1}{x ^{6}} d x

\int_{0}^{2} \frac{r}{4 - r ^{2}} d r

\int_{0}^{1} 6 x^{5} (2 - x^{6}) d x

\int_{0}^{1} cos (x) sin (x) d x